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Approximating the Cumulant Generating Function of Triangles in the Erdös–Rényi Random Graph J. Stat. Phys. (IF 1.243) Pub Date : 2021-01-25 Cristian Giardinà, Claudio Giberti, Elena Magnanini
We study the pressure of the “edge-triangle model”, which is equivalent to the cumulant generating function of triangles in the Erdös–Rényi random graph. The investigation involves a population dynamics method on finite graphs of increasing volume, as well as a discretization of the graphon variational problem arising in the infinite volume limit. As a result, we locate a curve in the parameter space
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Numerical Study of the Thermodynamic Uncertainty Relation for the KPZ-Equation J. Stat. Phys. (IF 1.243) Pub Date : 2021-01-25 Oliver Niggemann, Udo Seifert
A general framework for the field-theoretic thermodynamic uncertainty relation was recently proposed and illustrated with the \((1+1)\) dimensional Kardar–Parisi–Zhang equation. In the present paper, the analytical results obtained there in the weak coupling limit are tested via a direct numerical simulation of the KPZ equation with good agreement. The accuracy of the numerical results varies with
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Combined Mean-Field and Semiclassical Limits of Large Fermionic Systems J. Stat. Phys. (IF 1.243) Pub Date : 2021-01-25 Li Chen, Jinyeop Lee, Matthew Liew
We study the time dependent Schrödinger equation for large spinless fermions with the semiclassical scale \(\hbar = N^{-1/3}\) in three dimensions. By using the Husimi measure defined by coherent states, we rewrite the Schrödinger equation into a BBGKY type of hierarchy for the k particle Husimi measure. Further estimates are derived to obtain the weak compactness of the Husimi measure, and in addition
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Mathematics of Parking: Varying Parking Rate J. Stat. Phys. (IF 1.243) Pub Date : 2021-01-24 Pavel B. Dubovski, Michael Tamarov
In the classical parking problem, unit intervals (“car lengths”) are placed uniformly at random without overlapping. The process terminates at saturation, i.e. until no more unit intervals can be stowed. In this paper, we present a generalization of this problem in which the unit intervals are placed with an exponential distribution with rate parameter \(\lambda \). We show that the mathematical expectation
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Fixation for Two-Dimensional $${\mathcal {U}}$$ U -Ising and $${\mathcal {U}}$$ U -Voter Dynamics J. Stat. Phys. (IF 1.243) Pub Date : 2021-01-24 Daniel Blanquicett
Given a finite family \({\mathcal {U}}\) of finite subsets of \({\mathbb {Z}}^d\setminus \{0\}\), the \({\mathcal {U}}\)-voter dynamics in the space of configurations \(\{+,-\}^{{\mathbb {Z}}^d}\) is defined as follows: every \(v\in {\mathbb {Z}}^d\) has an independent exponential random clock, and when the clock at v rings, the vertex v chooses \(X\in {\mathcal {U}}\) uniformly at random. If the set
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Moments of Moments and Branching Random Walks J. Stat. Phys. (IF 1.243) Pub Date : 2021-01-12 E. C. Bailey, J. P. Keating
We calculate, for a branching random walk \(X_n(l)\) to a leaf l at depth n on a binary tree, the positive integer moments of the random variable \(\frac{1}{2^{n}}\sum _{l=1}^{2^n}e^{2\beta X_n(l)}\), for \(\beta \in {\mathbb {R}}\). We obtain explicit formulae for the first few moments for finite n. In the limit \(n\rightarrow \infty \), our expression coincides with recent conjectures and results
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The Upper Capacity Topological Entropy of Free Semigroup Actions for Certain Non-compact Sets J. Stat. Phys. (IF 1.243) Pub Date : 2021-01-09 Li Zhu, Dongkui Ma
In this paper, we first introduce some new notions of ‘periodic-like’ points, such as almost periodic points, weakly almost periodic points, quasi-weakly almost periodic points, of free semigroup actions. We find that the corresponding sets and gap-sets of these points carry full upper capacity topological entropy of free semigroup actions under certain conditions. Furthermore, \(\phi \)-irregular
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Effects of Random Excitations on the Dynamical Response of Duffing Systems J. Stat. Phys. (IF 1.243) Pub Date : 2021-01-09 Kajal Krishna Dey, Golam Ali Sekh
We study the dynamics of a Duffing oscillator excited by correlated random perturbations for both fixed and periodically modulated stiffness. In the case of fixed stiffness we see that Poincaré map gets distorted due to the random excitation and, the distortion increases with the increase of correlation of the field. In a strongly correlated field, however, the map becomes purely random. We analyse
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Thermal Ionization for Short-Range Potentials J. Stat. Phys. (IF 1.243) Pub Date : 2021-01-08 David Hasler, Oliver Siebert
We study a concrete model of a confined particle in form of a Schrödinger operator with a compactly supported smooth potential coupled to a bosonic field at positive temperature. We show, that the model exhibits thermal ionization for any positive temperature, provided the coupling is sufficiently small. Mathematically, one has to rule out that zero is an eigenvalue of the self-adjoint generator of
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Invariant Measure for Infinite Weakly Hyperbolic Iterated Function Systems J. Stat. Phys. (IF 1.243) Pub Date : 2021-01-07 Xiaopeng Chen, Chang-Bing Li, Yuan-Ling Ye
In this paper we define infinite weakly hyperbolic iterated function systems associated with uniformly Dini continuous weight functions. We study the Ruelle operator theorem for the infinite weakly hyperbolic iterated function systems associated with uniformly Dini continuous weight functions. We prove the existence and uniqueness of the invariant measure for these type systems.
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Long-Time Anderson Localization for the Nonlinear Schrödinger Equation Revisited J. Stat. Phys. (IF 1.243) Pub Date : 2021-01-07 Hongzi Cong, Yunfeng Shi, Zhifei Zhang
In this paper, we confirm the conjecture of Wang and Zhang (J Stat Phys 134 (5-6):953–968, 2009) in a long time scale, i.e., the displacement of the wavefront for 1D nonlinear random Schrödinger equation is of logarithmic order in time |t|.
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Quantum Statistical Learning via Quantum Wasserstein Natural Gradient J. Stat. Phys. (IF 1.243) Pub Date : 2021-01-07 Simon Becker, Wuchen Li
In this article, we introduce a new approach towards the statistical learning problem \(\mathrm{argmin}_{\rho (\theta ) \in {\mathcal {P}}_{\theta }} W_{Q}^2 (\rho _{\star },\rho (\theta ))\) to approximate a target quantum state \(\rho _{\star }\) by a set of parametrized quantum states \(\rho (\theta )\) in a quantum \(L^2\)-Wasserstein metric. We solve this estimation problem by considering Wasserstein
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Ferromagnetism in d -Dimensional SU( n ) Hubbard Models with Nearly Flat Bands J. Stat. Phys. (IF 1.243) Pub Date : 2021-01-07 Kensuke Tamura, Hosho Katsura
We present rigorous results for the SU(n) Fermi–Hubbard models with finite-range hopping in d (\(\ge 2\)) dimensions. The models are defined on a class of decorated lattices. We first study the models with flat bands at the bottom of the single-particle spectrum and prove that the ground states exhibit SU(n) ferromagnetism when the number of particles is equal to the number of unit cells. We then perturb
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Hyperbolic Polygonal Billiards Close to 1-Dimensional Piecewise Expanding Maps J. Stat. Phys. (IF 1.243) Pub Date : 2021-01-07 Gianluigi Del Magno, João Lopes Dias, Pedro Duarte, José Pedro Gaivão
We consider polygonal billiards with collisions contracting the reflection angle towards the normal to the boundary of the table. In previous work, we proved that such billiards have a finite number of ergodic SRB measures supported on hyperbolic generalized attractors. Here we study the relation of these measures with the ergodic absolutely continuous invariant probabilities (acips) of the slap map
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Large Deviations in the Symmetric Simple Exclusion Process with Slow Boundaries J. Stat. Phys. (IF 1.243) Pub Date : 2021-01-07 Bernard Derrida, Ori Hirschberg, Tridib Sadhu
We obtain the exact large deviation functions of the density profile and of the current, in the non-equilibrium steady state of a one dimensional symmetric simple exclusion process coupled to boundary reservoirs with slow rates. Compared to earlier results, where rates at the boundaries are comparable to the bulk ones, we show how macroscopic fluctuations are modified when the boundary rates are slower
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Behavior of the Lattice Gaussian Free Field with Weak Repulsive Potentials J. Stat. Phys. (IF 1.243) Pub Date : 2021-01-07 Hironobu Sakagawa
We consider the \(d\ (\ge 3)\) - dimensional lattice Gaussian free field on \(\varLambda _N :=[-N, N]^d\cap \mathbb {Z}^d\) in the presence of a self-potential of the form \(U(r)= -b I(|r|\le a)\), \(a>0, b\in \mathbb {R}\). When \(b>0\), the potential attracts the field to the level around zero and is called square-well pinning. It is known that the field turns to be localized and massive for every
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Diagonalizability of Quantum Markov States on Trees J. Stat. Phys. (IF 1.243) Pub Date : 2021-01-07 Farrukh Mukhamedov, Abdessatar Souissi
We introduce quantum Markov states (QMS) in a general tree graph \(G= (V, E)\), extending the Cayley tree’s case. We investigate the Markov property w.r.t. the finer structure of the considered tree. The main result of the present paper concerns the diagonalizability of a locally faithful QMS \(\varphi \) on a UHF-algebra \({\mathcal {A}}_V\) over the considered tree by means of a suitable conditional
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Condensation and Extremes for a Fluctuating Number of Independent Random Variables J. Stat. Phys. (IF 1.243) Pub Date : 2021-01-07 Claude Godrèche
We address the question of condensation and extremes for three classes of intimately related stochastic processes: (a) random allocation models and zero-range processes, (b) tied-down renewal processes, (c) free renewal processes. While for the former class the number of components of the system is fixed, for the two other classes it is a fluctuating quantity. Studies of these topics are scattered
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Slow Propagation in Some Disordered Quantum Spin Chains J. Stat. Phys. (IF 1.243) Pub Date : 2021-01-07 Bruno Nachtergaele, Jake Reschke
We introduce the notion of transmission time to study the dynamics of disordered quantum spin chains and prove results relating its behavior to many-body localization properties. We also study two versions of the so-called Local Integrals of Motion (LIOM) representation of spin chain Hamiltonians and their relation to dynamical many-body localization. We prove that uniform-in-time dynamical localization
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Exact Recovery of Community Detection in k -Partite Graph Models with Applications to Learning Electric Potentials in Electric Networks J. Stat. Phys. (IF 1.243) Pub Date : 2021-01-04 Zhongyang Li
We study the vertex classification problem on a graph whose vertices are in \(k\ (k\ge 2)\) different communities, edges are only allowed between distinct communities, and the number of vertices in different communities are not necessarily equal. The observation is a weighted adjacency matrix, perturbed by a scalar multiple of the Gaussian Orthogonal Ensemble (GOE), or Gaussian Unitary Ensemble (GUE)
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Cooperative Dynamics in Bidirectional Transport on Flexible Lattice J. Stat. Phys. (IF 1.243) Pub Date : 2021-01-02 Akriti Jindal, Atul Kumar Verma, Arvind Kumar Gupta
Several theoretical models based on totally asymmetric simple exclusion process (TASEP) have been extensively utilized to study various non-equilibrium transport phenomena. Inspired by the the role of microtubule-transported vesicles in intracellular transport, we propose a generalized TASEP model, where two distinct particles are directed to hop stochastically in opposite directions on a flexible
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Derivation of Multicomponent Lattice Boltzmann Equations by Introducing a Nonequilibrium Distribution Function into the Maxwell Iteration Based on the Convective Scaling J. Stat. Phys. (IF 1.243) Pub Date : 2021-01-02 Keiichi Yamamoto, Takeshi Seta
This study firstly proposes a simple recursive method for deriving the macroscale equations from lattice Boltzmann equations. Similar to the Maxwell iteration based on the convective scaling, this method is used to expand the lattice Boltzmann (LB) equations with the time step \(\delta _{t}\). It is characterised by the incorporation of a nonequilibrium distribution function not appearing in the Maxwell
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The Multi-species Mean-Field Spin-Glass on the Nishimori Line J. Stat. Phys. (IF 1.243) Pub Date : 2021-01-02 Diego Alberici, Francesco Camilli, Pierluigi Contucci, Emanuele Mingione
In this paper we study a multi-species disordered model on the Nishimori line. The typical properties of this line, a set of identities and inequalities among correlation functions, allow us to prove the replica symmetry i.e. the concentration of the order parameter. When the interaction structure is elliptic we rigorously compute the exact solution of the model in terms of a finite-dimensional variational
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Cluster Size Distribution in a System of Randomly Spaced Particles J. Stat. Phys. (IF 1.243) Pub Date : 2021-01-02 M. Kh. Khokonov, A. Kh. Khokonov
The distribution function of particles over clusters is proposed for a system of identical intersecting spheres, the centers of which are uniformly distributed in space. Consideration is based on the concept of the rank number of clusters, where the rank is assigned to clusters according to the cluster sizes. The distribution function does not depend on boundary conditions and is valid for infinite
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Quantum Hamiltonians with Weak Random Abstract Perturbation. II. Localization in the Expanded Spectrum J. Stat. Phys. (IF 1.243) Pub Date : 2021-01-01 Denis Borisov, Matthias Täufer, Ivan Veselić
We consider multi-dimensional Schrödinger operators with a weak random perturbation distributed in the cells of some periodic lattice. In every cell the perturbation is described by the translate of a fixed abstract operator depending on a random variable. The random variables, indexed by the lattice, are assumed to be independent and identically distributed according to an absolutely continuous probability
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Cucker–Smale Type Dynamics of Infinitely Many Individuals with Repulsive Forces J. Stat. Phys. (IF 1.243) Pub Date : 2020-10-22 Paolo Buttà, Carlo Marchioro
We study the existence and uniqueness of the time evolution of a system of infinitely many individuals, moving in a tunnel and subjected to a Cucker–Smale type alignment dynamics with compactly supported communication kernels and to short-range repulsive interactions to avoid collisions.
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On the Schrödinger–Lohe Hierarchy for Aggregation and Its Emergent Dynamics J. Stat. Phys. (IF 1.243) Pub Date : 2020-10-22 Seung-Yeal Ha, Hansol Park
The Lohe hierarchy is a hierarchy of finite-dimensional aggregation models consisting of the Kuramoto model, the complex Lohe sphere model, the Lohe matrix model and the Lohe tensor model. In contrast, the Schrödinger–Lohe model is the only known infinite-dimensional Lohe aggregation model in literature. In this paper, we provide an explicit connection between the Schrödinger–Lohe model and the complex
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On the General Properties of Non-linear Optical Conductivities J. Stat. Phys. (IF 1.243) Pub Date : 2020-10-18 Haruki Watanabe, Yankang Liu, Masaki Oshikawa
The optical conductivity is the basic defining property of materials characterizing the current response toward time-dependent electric fields. In this work, following the approach of Kubo’s response theory, we study the general properties of the nonlinear optical conductivities of quantum many-body systems both in equilibrium and non-equilibrium. We obtain an expression of the second- and the third-order
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Correction to: Non-commutative Calculus, Optimal Transport and Functional Inequalities in Dissipative Quantum Systems J. Stat. Phys. (IF 1.243) Pub Date : 2020-11-18 Eric A. Carlen, Jan Maas
We correct an incorrect constant in the statement of Theorem 10.6.
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Distance from the Nucleus to a Uniformly Random Point in the 0-Cell and the Typical Cell of the Poisson–Voronoi Tessellation J. Stat. Phys. (IF 1.243) Pub Date : 2020-10-22 Praful D. Mankar, Priyabrata Parida, Harpreet S. Dhillon, Martin Haenggi
Consider the distances \(\tilde{R}_o\) and \(R_o\) from the nucleus to a uniformly random point in the 0-cell and the typical cell, respectively, of the d-dimensional Poisson–Voronoi (PV) tessellation. The main objective of this paper is to characterize the exact distributions of \(\tilde{R}_o\) and \(R_o\). First, using the well-known relationship between the 0-cell and the typical cell, we show that
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On the Cutoff Approximation for the Boltzmann Equation with Long-Range Interaction J. Stat. Phys. (IF 1.243) Pub Date : 2020-10-22 Ling-Bing He, Jin-Cheng Jiang, Yu-Long Zhou
The Boltzmann collision operator for long-range interactions is usually employed in its “weak form” in the literature. However the weak form utilizes the symmetry property of the spherical integral and thus should be understood more or less in the principle value sense especially for strong angular singularity. To study the integral in the Lebesgue sense, it is natural to define the collision operator
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Edge Scaling Limit of the Spectral Radius for Random Normal Matrix Ensembles at Hard Edge J. Stat. Phys. (IF 1.243) Pub Date : 2020-09-16 Seong-Mi Seo
We investigate local statistics of eigenvalues for random normal matrices, represented as 2D determinantal Coulomb gases, in the case when the eigenvalues are forced to be in the support of the equilibrium measure associated with an external field. For radially symmetric external fields with sufficient growth at infinity, we show that the fluctuations of the spectral radius around a hard edge tend
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Eigenvalues Outside the Bulk of Inhomogeneous Erdős–Rényi Random Graphs J. Stat. Phys. (IF 1.243) Pub Date : 2020-09-26 Arijit Chakrabarty, Sukrit Chakraborty, Rajat Subhra Hazra
In this article, an inhomogeneous Erdős–Rényi random graph on \(\{1,\ldots , N\}\) is considered, where an edge is placed between vertices i and j with probability \(\varepsilon _N f(i/N,j/N)\), for \(i\le j\), the choice being made independently for each pair. The integral operator \(I_f\) associated with the bounded function f is assumed to be symmetric, non-negative definite, and of finite rank
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Typical Ground States for Large Sets of Interactions J. Stat. Phys. (IF 1.243) Pub Date : 2020-09-29 Aernout van Enter, Jacek Miȩkisz
We discuss what ground states for generic interactions look like. We note that a recent result, due to Morris, implies that the behaviour of ground-state measures for generic interactions is similar to that of generic measures. In particular, it follows from his observation that they have singular spectrum and that they are weak mixing, but not mixing.
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The Asymptotics of the Clustering Transition for Random Constraint Satisfaction Problems J. Stat. Phys. (IF 1.243) Pub Date : 2020-10-24 Louise Budzynski, Guilhem Semerjian
Random constraint satisfaction problems exhibit several phase transitions when their density of constraints is varied. One of these threshold phenomena, known as the clustering or dynamic transition, corresponds to a transition for an information theoretic problem called tree reconstruction. In this article we study this threshold for two CSPs, namely the bicoloring of k-uniform hypergraphs with a
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Attraction of Like-Charged Walls with Counterions Only: Exact Results for the 2D Cylinder Geometry J. Stat. Phys. (IF 1.243) Pub Date : 2020-09-29 Ladislav Šamaj
We study a 2D system of identical mobile particles on the surface of a cylinder of finite length d and circumference W, immersed in a medium of dielectric constant \(\varepsilon \). The two end-circles of the cylinder are like-charged with the fixed uniform charge densities, the particles of opposite charge \(-e\) (e being the elementary charge) are coined as “counterions”; the system as a whole is
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Random Motion of Light-Speed Particles J. Stat. Phys. (IF 1.243) Pub Date : 2020-09-28 Maurizio Serva
In 1956 Mark Kac proposed a process related to the telegrapher equation where the particle travels at constant speed (say the speed of light c) and randomly inverts its velocity. This process had important applications concerning the path-integral solution and the probabilistic interpretation of the 1\(+\)1 dimensions Dirac equation. The extension to 3\(+\)1 dimensions requires that the particle only
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Linear Response Theory and Entropic Fluctuations in Repeated Interaction Quantum Systems J. Stat. Phys. (IF 1.243) Pub Date : 2020-09-25 Jean-François Bougron, Laurent Bruneau
We study linear response theory and entropic fluctuations of finite dimensional non-equilibrium Repeated Interaction Systems (RIS). More precisely, in a situation where the temperatures of the probes can take a finite number of different values, we prove analogs of the Green–Kubo fluctuation–dissipation formula and Onsager reciprocity relations on energy flux observables. Then we prove a Large Deviation
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Averaging Principle for Multiscale Stochastic Fractional Schrödinger–Korteweg-de Vries System J. Stat. Phys. (IF 1.243) Pub Date : 2020-09-27 Peng Gao
This work concerns the averaging principle for multiscale stochastic fractional Schrödinger–Korteweg-de Vries system. Stochastic averaging principle is a powerful tool for studying qualitative analysis of stochastic dynamical systems with different time-scales. To be more precise, under suitable conditions, the multiscale system can be reduced to a single stochastic fractional Korteweg-de Vries equation
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Parameter Symmetry in Perturbed GUE Corners Process and Reflected Drifted Brownian Motions J. Stat. Phys. (IF 1.243) Pub Date : 2020-10-22 Leonid Petrov, Mikhail Tikhonov
The perturbed GUE corners ensemble is the joint distribution of eigenvalues of all principal submatrices of a matrix \(G+\mathrm {diag}(\mathbf {a})\), where G is the random matrix from the Gaussian Unitary Ensemble (GUE), and \(\mathrm {diag}(\mathbf {a})\) is a fixed diagonal matrix. We introduce Markov transitions based on exponential jumps of eigenvalues, and show that their successive application
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On the Mean-Field Limit for the Vlasov–Poisson–Fokker–Planck System J. Stat. Phys. (IF 1.243) Pub Date : 2020-10-18 Hui Huang, Jian-Guo Liu, Peter Pickl
We rigorously justify the mean-field limit of an N-particle system subject to Brownian motions and interacting through the Newtonian potential in \({\mathbb {R}}^3\). Our result leads to a derivation of the Vlasov–Poisson–Fokker–Planck (VPFP) equations from the regularized microscopic N-particle system. More precisely, we show that the maximal distance between the exact microscopic trajectories and
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Sunklodas’ Approach to Normal Approximation for Time-Dependent Dynamical Systems J. Stat. Phys. (IF 1.243) Pub Date : 2020-09-25 Juho Leppänen, Mikko Stenlund
We consider time-dependent dynamical systems arising as sequential compositions of self-maps of a probability space. We establish conditions under which the Birkhoff sums for multivariate observations, given a centering and a general normalizing sequence b(N) of invertible square matrices, are approximated by a normal distribution with respect to a metric of regular test functions. Depending on the
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The Rate of Convergence for the Smoluchowski-Kramers Approximation for Stochastic Differential Equations with FBM J. Stat. Phys. (IF 1.243) Pub Date : 2020-09-25 Ta Cong Son
In this paper, we study the rate in the Smoluchowski–Kramers approximation for the solution of the equation \(X_t=x+B_t^H+\int _0^t b(X_s)ds\) where \(\{B_t^H, t\in [0,T]\}\) is a fractional Brownian motion with Hurst parameter \(H\in \big (\frac{1}{2},1\big )\). Based on the techniques of Malliavin calculus, we provide an explicit bound on total variation distance for the rate of convergence.
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Intermediate Disorder Regime for Half-Space Directed Polymers J. Stat. Phys. (IF 1.243) Pub Date : 2020-11-17 Xuan Wu
We consider the convergence of point-to-point partition functions for the half-space directed polymer model in dimension 1+1 in the intermediate disorder regime as introduced for the full space model by Alberts, Khanin and Quastel in [1]. By scaling the inverse temperature as \(\beta n^{-1/4}\), the point-to-point partition function converges to the chaos series for the solution to stochastic heat
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Uniqueness of Minimizer for Countable Markov Shifts and Equidistribution of Periodic Points J. Stat. Phys. (IF 1.243) Pub Date : 2020-11-10 Hiroki Takahasi
For a finitely irreducible countable Markov shift and a potential with summable variations, we provide a condition on the associated pressure function which ensures that Bowen’s Gibbs state, the equilibrium state, and the minimizer of the level-2 large deviations rate function are all unique and they coincide. From this, we deduce that the set of periodic points weighted with the potential equidistributes
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Cycles in Random Meander Systems J. Stat. Phys. (IF 1.243) Pub Date : 2020-11-09 Vladislav Kargin
A meander system is a union of two arc systems that represent non-crossing pairings of the set \([2n] = \{1, \ldots , 2n\}\) in the upper and lower half-plane. In this paper, we consider random meander systems. We show that for a class of random meander systems,—for simply-generated meander systems,—the number of cycles in a system of size n grows linearly with n and that the length of the largest
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Simulation Studies of Random Sequential Adsorption (RSA) of Mixture of Two-Component Circular Discs J. Stat. Phys. (IF 1.243) Pub Date : 2020-11-06 K. V. Wagaskar, Ravikiran Late, A. G. Banpurkar, A. V. Limaye, Pradip B. Shelke
We study Random Sequential Adsorption (RSA) of mixture of two-component circular discs on a two-dimensional continuum substrate by computer simulation for different values of radius ratio \({r}_{A}/{r}_{B}\), \(({r}_{A}<{r}_{B})\), and relative rate constant \(k = {k}_{A}/{k}_{B}\) between the discs. For smaller values of radius ratio and all values of relative rate constant between the discs, the
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Modeling of Chemical Reaction Systems with Detailed Balance Using Gradient Structures J. Stat. Phys. (IF 1.243) Pub Date : 2020-11-06 Jan Maas, Alexander Mielke
We consider various modeling levels for spatially homogeneous chemical reaction systems, namely the chemical master equation, the chemical Langevin dynamics, and the reaction-rate equation. Throughout we restrict our study to the case where the microscopic system satisfies the detailed-balance condition. The latter allows us to enrich the systems with a gradient structure, i.e. the evolution is given
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On the Number of Limit Cycles in Diluted Neural Networks J. Stat. Phys. (IF 1.243) Pub Date : 2020-11-05 Sungmin Hwang, Enrico Lanza, Giorgio Parisi, Jacopo Rocchi, Giancarlo Ruocco, Francesco Zamponi
We consider the storage properties of temporal patterns, i.e. cycles of finite lengths, in neural networks represented by (generally asymmetric) spin glasses defined on random graphs. Inspired by the observation that dynamics on sparse systems has more basins of attractions than the dynamics of densely connected ones, we consider the attractors of a greedy dynamics in sparse topologies, considered
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Analytical Survival Analysis of the Ornstein–Uhlenbeck Process J. Stat. Phys. (IF 1.243) Pub Date : 2020-11-05 L. T. Giorgini, W. Moon, J. S. Wettlaufer
We use asymptotic methods from the theory of differential equations to obtain an analytical expression for the survival probability of an Ornstein–Uhlenbeck process with a potential defined over a broad domain. We form a uniformly continuous analytical solution covering the entire domain by asymptotically matching approximate solutions in an interior region, centered around the origin, to those in
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A Note on the Spectral Gap of the Fredrickson–Andersen One Spin Facilitated Model J. Stat. Phys. (IF 1.243) Pub Date : 2020-11-04 Assaf Shapira
This note discusses the spectral gap of the Fredrickson–Andersen one spin facilitated model in two different settings. The model describes an interacting particle system on a graph, where each site is either occupied or empty; and a site may change its occupation when at least one of its neighbors is empty. We will first consider the model on the infinite lattice \({\mathbb {Z}}^{d}\), with density
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Correction to: Optimal Estimate of the Spectral Gap for the Degenerate Goldstein-Taylor Model J. Stat. Phys. (IF 1.243) Pub Date : 2020-09-14 Étienne Bernard, Francesco Salvarani
In [1], on p. 366, line 5 and on p. 369, line 12, replace
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On the Law of Large Numbers for the Empirical Measure Process of Generalized Dyson Brownian Motion J. Stat. Phys. (IF 1.243) Pub Date : 2020-09-21 Songzi Li, Xiang-Dong Li, Yong-Xiao Xie
We study the generalized Dyson Brownian motion (GDBM) of an interacting N-particle system with logarithmic Coulomb interaction and general potential V. Under reasonable condition on V, we prove the existence and uniqueness of strong solution to SDE for GDBM. We then prove that the family of the empirical measures of GDBM is tight on \(\mathcal {C}([0,T],\mathscr {P}(\mathbb {R}))\) and all the large
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Voter and Majority Dynamics with Biased and Stubborn Agents J. Stat. Phys. (IF 1.243) Pub Date : 2020-08-20 Arpan Mukhopadhyay, Ravi R. Mazumdar, Rahul Roy
We study binary opinion dynamics in a fully connected network of interacting agents. The agents are assumed to interact according to one of the following rules: (1) Voter rule: An updating agent simply copies the opinion of another randomly sampled agent; (2) Majority rule: An updating agent samples multiple agents and adopts the majority opinion in the selected group. We focus on the scenario where
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Moderate Deviation and Exit Time Estimates for Stationary Last Passage Percolation J. Stat. Phys. (IF 1.243) Pub Date : 2020-09-09 Manan Bhatia
We consider planar stationary exponential last passage percolation in the positive quadrant with boundary weights. For \(\rho \in (0,1)\) and points \(v_N=( (1-\rho )^2 N, \rho ^2 N)\) going to infinity along the characteristic direction, we establish right tail estimates with the optimal exponent for the exit time of the geodesic, along with optimal exponent estimates for the upper tail moderate deviations
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The Maki-Thompson Rumor Model on Infinite Cayley Trees J. Stat. Phys. (IF 1.243) Pub Date : 2020-08-13 Valdivino V. Junior, Pablo M. Rodriguez, Adalto Speroto
In this paper we study the Maki-Thompson rumor model on infinite Cayley trees. The basic version of the model is defined by assuming that a population represented by a graph is subdivided into three classes of individuals: ignorants, spreaders and stiflers. A spreader tells the rumor to any of its (nearest) ignorant neighbors at rate one. At the same rate, a spreader becomes a stifler after a contact
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Loop-Erased Random Walk as a Spin System Observable J. Stat. Phys. (IF 1.243) Pub Date : 2020-08-24 Tyler Helmuth, Assaf Shapira
The determination of the Hausdorff dimension of the scaling limit of loop-erased random walk is closely related to the study of the one-point function of loop-erased random walk, i.e., the probability a loop-erased random walk passes through a given vertex. Recent work in the theoretical physics literature has investigated the Hausdorff dimension of loop-erased random walk in three dimensions by applying
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Point Processes of Non stationary Sequences Generated by Sequential and Random Dynamical Systems J. Stat. Phys. (IF 1.243) Pub Date : 2020-09-04 Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, Mário Magalhães, Sandro Vaienti
We give general sufficient conditions to prove the convergence of marked point processes that keep record of the occurrence of rare events and of their impact for non-autonomous dynamical systems. We apply the results to sequential dynamical systems associated to both uniformly and non-uniformly expanding maps and to random dynamical systems given by fibred Lasota Yorke maps.
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Multidimensional Walks with Random Tendency J. Stat. Phys. (IF 1.243) Pub Date : 2020-09-26 Manuel González-Navarrete
We introduce a multidimensional walk with memory and random tendency. The asymptotic behaviour is characterized, proving a law of large numbers and showing a phase transition from diffusive to superdiffusive regimes. In first case, we obtain a functional limit theorem to Gaussian vectors. In superdiffusive regime, we obtain strong convergence to a non-Gaussian random vector and characterize its moments
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Hydrodynamics for SSEP with Non-reversible Slow Boundary Dynamics: Part I, the Critical Regime and Beyond J. Stat. Phys. (IF 1.243) Pub Date : 2020-09-18 C. Erignoux, P. Gonçalves, G. Nahum
The purpose of this article is to provide a simple proof of the hydrodynamic and hydrostatic behavior of the SSEP in contact with slowed reservoirs which inject and remove particles in a finite size windows at the extremities of the bulk. More precisely, the reservoirs inject/remove particles at/from any point of a window of size K placed at each extremity of the bulk and particles are injected/removed
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