We consider the assignment problem between two sets of N random points on a smooth, two-dimensional manifold \(\Omega \) of unit area. It is known that the average cost scales as \(E_{\Omega }(N)\sim {1}/{2\pi }\ln N\) with a correction that is at most of order \(\sqrt{\ln N\ln \ln N}\). In this paper, we show that, within the linearization approximation of the field-theoretical formulation of the

The structure function of a random matrix ensemble can be specified in terms of the covariance of the linear statistics \(\sum _{j=1}^N e^{i k_1 \lambda _j}\), \(\sum _{j=1}^N e^{-i k_2 \lambda _j}\) for Hermitian matrices, and the same with the eigenvalues \(\lambda _j\) replaced by the eigenangles \(\theta _j\) for unitary matrices. As such it can be written in terms of the Fourier transform of the

Hidden Markov chains are widely applied statistical models of stochastic processes, from fundamental physics and chemistry to finance, health, and artificial intelligence. The hidden Markov processes they generate are notoriously complicated, however, even if the chain is finite state: no finite expression for their Shannon entropy rate exists, as the set of their predictive features is generically

We analyze the free energy and the overlaps in the 2-spin spherical Sherrington Kirkpatrick spin glass model with an external field for the purpose of understanding the transition between this model and the one without an external field. We compute the limiting values and fluctuations of the free energy as well as three types of overlaps in the setting where the strength of the external field goes

We consider stochastic growth models to represent population dynamics subject to geometric catastrophes. We analyze different dispersion schemes after catastrophes, to study how these schemes impact the population viability and comparing them with the scheme where there is no dispersion. In the schemes with dispersion, we consider that each colony, after the catastrophe event, has d new positions to

This paper deals with the renormalization of symmetric bimodal maps with low smoothness. We prove the existence of the renormalization fixed point in the space \(C ^{1+Lip}\) symmetric bimodal maps. Moreover, we show that the topological entropy of the renormalization operator defined on the space of \(C^{1+Lip}\) symmetric bimodal maps is infinite. Further we prove the existence of a continuum of

We consider Kac’s 1D N-particle system coupled to an ideal thermostat at a fixed temperature, introduced by Bonetto, Loss, and Vaidyanathan in 2014. We obtain a propagation of chaos result for this system, with an explicit and uniform-in-time rate of order \(N^{-1/3}\) in terms of the 2-Wasserstein metric squared. We also show well-posedness and equilibration for the limit kinetic equation in the space

The goal of this paper is to extend the existence result of measure-valued solution to the Boltzmann equation in elastic interaction, given by Morimoto–Wang–Yang in (J Stat Phys 165:866–906, 2016), to the inelastic Boltzmann equation with moderately soft potentials, which is also an extensive work of our preceding result in the inelastic Maxwellian molecules case. We first prove the existence and uniqueness

We study the macroscopic profiles of temperature and angular momentum in the stationary state of chains of rotors under a thermo-mechanical forcing applied at the boundaries. These profiles are solutions of a system of diffusive partial differential equations with boundary conditions determined by the thermo-mechanical forcing. Instead of expensive Monte Carlo simulations of the underlying microscopic

In this paper we study coupled fast-slow ordinary differential equations (ODEs) with small time scale separation parameter \(\varepsilon \) such that, for every fixed value of the slow variable, the fast dynamics are sufficiently chaotic with ergodic invariant measure. Convergence of the slow process to the solution of a homogenized stochastic differential equation (SDE) in the limit \(\varepsilon

We consider the process of opinion formation, in a society where there is a set of rules B that indicates whether a social instance is acceptable. Public opinion is formed by the integration of the voters’ attitudes which can be either conservative (mostly in agreement with B) or liberal (mostly in disagreement with B and in agreement with peer voters). These attitudes are represented by stable fixed

We study the Bernstein–Landau paradox in the collisionless motion of an electrostatic plasma in the presence of a constant external magnetic field. The Bernstein–Landau paradox consists in that in the presence of the magnetic field, the electric field and the charge density fluctuation have an oscillatory behavior in time. This is radically different from Landau damping, in the case without magnetic

This study extends a prior investigation of limit shapes for grand canonical Gibbs ensembles of partitions of integers, which was based on analysis of sums of geometric random variables. Here we compute limit shapes for partitions of sets, which lead to the sums of Poisson random variables. Under mild monotonicity assumptions on the energy function, we derive all possible limit shapes arising from

The first part of this paper is devoted to study a model of one-dimensional random walk with memory to the maximum position described as follows. At each step the walker resets to the rightmost visited site with probability \(r \in (0,1)\) and moves as the simple random walk with remaining probability. Using the approach of renewal theory, we prove the laws of large numbers and the central limit theorems

We discuss a stochastic interacting particles’ system connected to dyadic models of turbulence, defining suitable classes of solutions and proving their existence and uniqueness. We investigate the regularity of a particular family of solutions, called moderate, and we conclude with existence and uniqueness of invariant measures associated with such moderate solutions.

Gaussian noise channels (also called classical noise channels, bosonic Gaussian channels) arise naturally in continuous variable quantum information and play an important role in both theoretical analysis and experimental investigation of information transmission. After reviewing concisely the basic properties of these channels, we introduce an information-theoretic measure for the decoherence of optical

We show that certain billiard flows on planar billiard tables with horns can be modeled as suspension flows over Young towers (Ann. Math. 147:585–650, 1998) with exponential tails. This implies exponential decay of correlations for the billiard map. Because the height function of the suspension flow itself is polynomial when the horns are Torricelli-like trumpets, one can derive Limit Laws for the

This paper is devoted to the analysis of Lindblad operators of Quantum Reset Models, describing the effective dynamics of tri-partite quantum systems subject to stochastic resets. We consider a chain of three independent subsystems, coupled by a Hamiltonian term. The two subsystems at each end of the chain are driven, independently from each other, by a reset Lindbladian, while the center system is

Nonequilibrium information thermodynamics determines the minimum energy dissipation to reliably erase memory under time-symmetric control protocols. We demonstrate that its bounds are tight and so show that the costs overwhelm those implied by Landauer’s energy bound on information erasure. Moreover, in the limit of perfect computation, the costs diverge. The conclusion is that time-asymmetric protocols

This paper explores the predictability of a Bak–Tang–Wiesenfeld isotropic sandpile on a self-similar lattice, introducing an algorithm which predicts the occurrence of target events when the stress in the system crosses a critical level. The model exhibits the self-organized critical dynamics characterized by the power-law segment of the size-frequency event distribution extended up to the sizes \(\sim

We are concerned with how the implementation of growth determines the expected number of state-changes in a growing self-organizing process. With this problem in mind, we examine two versions of the voter model on a one-dimensional growing lattice. Our main result asserts that the expected number of state-changes before an absorbing state is found can be controlled by balancing the conservative and

A correction to this paper has been published: https://doi.org/10.1007/s10955-021-02743-z

We examine the duality relating the equilibrium dynamics of the mean-field p-spin ferromagnets at finite size in the Guerra’s interpolation scheme and the Burgers hierarchy. In particular, we prove that—for fixed p—the expectation value of the order parameter on the first side w.r.t. the generalized partition function satisfies the \(p-1\)-th element in the aforementioned class of nonlinear equations

It has been established that the inclusive work for classical, Hamiltonian dynamics is equivalent to the two-time energy measurement paradigm in isolated quantum systems. However, a plethora of other notions of quantum work has emerged, and thus the natural question arises whether any other quantum notion can provide motivation for purely classical considerations. In the present analysis, we propose

In this paper, we present new estimates for the entropy dissipation of the Landau–Fermi–Dirac equation (with hard or moderately soft potentials) in terms of a weighted relative Fisher information adapted to this equation. Such estimates are used for studying the large time behaviour of the equation, as well as for providing new a priori estimates (in the soft potential case). An important feature of

We study completely separable states of the Lohe tensor model and their asymptotic collective dynamics. Here, the completely separable state means that it is a tensor product of rank-1 tensors. For the generalized Lohe matrix model corresponding to the Lohe tensor model for rank-2 tensors with the same size, we observe that the component rank-1 tensors of the completely separable states satisfy the

We present a three-lane exclusion process that exhibits the same universal fluctuation pattern as generic one-dimensional Hamiltonian dynamics with short-range interactions, viz., with two sound modes in the Kardar-Parisi-Zhang (KPZ) universality class (with dynamical exponent \(z=3/2\) and symmetric Prähofer-Spohn scaling function) and a superdiffusive heat mode with dynamical exponent \(z=5/3\) and

In this paper we investigate the long-time behavior of the subordination of the constant speed traveling waves by a general class of kernels. We use the Feller–Karamata Tauberian theorem in order to study the long-time behavior of the upper and lower wave. As a result we obtain the long-time behavior for the propagation of the front of the wave.

We construct a new mesoscopic model for granular media using Dynamical Density Functional Theory (DDFT). The model includes both a collision operator to incorporate inelasticity and the Helmholtz free energy functional to account for external potentials, interparticle interactions and volume exclusion. We use statistical data from event-driven microscopic simulations to determine the parameters not

A correction to this paper has been published: https://doi.org/10.1007/s10955-021-02742-0

We determine universal critical exponents that describe the continuous phase transitions in different dimensions of space. We use continued functions without any external unknown parameters to obtain analytic continuation for the recently derived 7-loop weak coupling \(\epsilon \)-expansions from O(n)-symmetric \(\phi ^4\) field theory. Employing a new blended continued function, we obtain critical

We consider the Random Euclidean Assignment Problem in dimension \(d=1\), with linear cost function. In this version of the problem, in general, there is a large degeneracy of the ground state, i.e. there are many different optimal matchings (say, \(\sim \exp (S_N)\) at size N). We characterize all possible optimal matchings of a given instance of the problem, and we give a simple product formula for

We consider a system of classical particles confined in a box \(\varLambda \subset {\mathbb {R}}^d\) with zero boundary conditions interacting via a stable and regular pair potential. Based on the validity of the cluster expansion for the canonical partition function in the high temperature–low density regime we prove moderate and precise large deviations from the mean value of the number of particles

We consider a system of harmonic oscillators with short range interactions and we study their correlation functions when the initial data is sampled with respect to the Gibbs measure. Such correlation functions display rapid oscillations that travel through the chain. We show that the correlation functions always have two fastest peaks which move in opposite directions and decay at rate \(t^{-\frac{1}{3}}\)

We prove a mean field limit, a law of large numbers and a central limit theorem for a system of point vortices on the 2D torus at equilibrium with positive temperature. The point vortices are formal solutions of a class of equations generalising the Euler equations, and are also known in the literature as generalised inviscid SQG. The mean-field limit is a steady solution of the equations, the CLT

Roughening of interfaces implies the divergence of the interface width w with the system size L. For two-dimensional systems the divergence of \(w^2\) is linear in L. In the framework of a detailed capillary wave approximation and of statistical field theory we derive an expression for the asymptotic behaviour of \(w^2\), which differs from results in the literature. It is confirmed by Monte Carlo

We consider here a new family of processes which describe particles which only can move at the speed of light c in the ordinary 3D physical space. The velocity, which randomly changes direction, can be represented as a point on the surface of a sphere of radius c and its trajectories only may connect points of this variety. A process can be constructed both by considering jumps from one point to another

We study the point process W in \({\mathbb {R}}^d\) obtained by adding an independent Gaussian vector to each point in \({\mathbb {Z}}^d\). Our main concern is the asymptotic size of fluctuations of the linear statistics in the large volume limit, defined as $$\begin{aligned} N(h,R) = \sum _{w\in W} h\left( \frac{w}{R}\right) , \end{aligned}$$ where \(h\in \left( L^1\cap L^2\right) ({\mathbb {R}}^d)\)

This work presents an efficient numerical method to evaluate the free energy density and associated thermodynamic quantities of (quasi) one-dimensional classical systems, by combining the transfer operator approach with a numerical discretization of integral kernels using quadrature rules. For analytic kernels, the technique exhibits exponential convergence in the number of quadrature points. As demonstration

We extend two rigorous results of Aizenman, Lebowitz, and Ruelle in their pioneering paper of 1987 on the Sherrington–Kirkpatrick spin-glass model without external magnetic field to the quantum case with a “transverse field” of strength \(\mathsf {b}\). More precisely, if the Gaussian disorder is weak in the sense that its standard deviation \(\mathsf {v}>0\) is smaller than the temperature \(1/\beta

One-dimensional edges of classical systems in two dimension sometimes show surprisingly rich phase transitions and critical phenomena, particularly when the bulk is at criticality. As such a model, we study the surface critical behavior of the 3-state dilute Potts model whose bulk is tuned at the tricritical point. To investigate it more precisely than in the previous works (Deng and Blöte, Phys Rev

We discuss the combined effects of overdamped motion in a quenched random potential and diffusion, in one dimension, in the limit where the diffusion coefficient is small. Our analysis considers the statistics of the mean first-passage time T(x) to reach position x, arising from different realisations of the random potential. Specifically, we contrast the median \({\bar{T}}(x)\), which is an informative

We present criteria for statistical stability of attracting sets for vector fields using dynamical conditions on the corresponding generated flows. These conditions are easily verified for all singular-hyperbolic attracting sets of \(C^2\) vector fields using known results, providing robust examples of statistically stable singular attracting sets (encompassing in particular the Lorenz and geometrical

Recently authors have introduced the idea of training discrete weights neural networks using a mix between classical simulated annealing and a replica ansatz known from the statistical physics literature. Among other points, they claim their method is able to find robust configurations. In this paper, we analyze this so called “replicated simulated annealing” algorithm. In particular, we give criteria

We derive the existence of infinite level GREM-like K-processes by taking the limit of a sequence of finite level versions of such processes as the number of levels diverges. The main step in the derivation is obtaining the convergence of the sequence of underlying finite level clock processes. This is accomplished by perturbing these processes so as to turn them into martingales, and resorting to

We consider the abelian stochastic sandpile model. In this model, a site is deemed unstable when it contains more than one particle. Each unstable site, independently, is toppled at rate 1, sending two of its particles to neighbouring sites chosen independently. We show that when the initial average density is less than 1/2, the system locally fixates almost surely. We achieve this bound by analysing

Weber–Fechner laws are phenomenological relations describing a logarithmic relation between perception and sensory stimulus in a great variety of organisms. While firmly established, a theoretical argument for those laws in terms of relevant models or from statistical physics is largely missing. We present such a discussion in terms of response theory for nonequilibrium systems, where the induced displacement

We consider the one dimensional symmetric simple exclusion process with a slow bond. In this model, particles cross each bond at rate \(N^2\), except one particular bond, the slow bond, where the rate is N. Above, N is the scaling parameter. This model has been considered in the context of hydrodynamic limits, fluctuations and large deviations. We investigate moderate deviations from hydrodynamics

Dynamical systems with \(\varepsilon \) small random perturbations appear in both continuous mechanical motions and discrete stochastic chemical kinetics. The present work provides a detailed analysis of the central limit theorem (CLT), with a time-inhomogeneous Gaussian process, near a deterministic limit cycle in \(\mathbb {R}^n\). Based on respectively the theory of random perturbations of dynamical

We generalize an idea in the works of Landauer and Bennett on computations, and Hill’s in chemical kinetics, to emphasize the importance of kinetic cycles in mesoscopic nonequilibrium thermodynamics (NET). For continuous stochastic systems, a NET in phase space is formulated in terms of cycle affinity \(\nabla \wedge \big (\mathbf{D}^{-1}\mathbf{b}\big )\) and vorticity potential \(\mathbf{A}(\mathbf{x})\)

We consider fast oscillating random perturbations of dynamical systems in regions where one can introduce action-angle-type coordinates. In an appropriate time scale, the evolution of first integrals, under the assumption that the set of resonance tori is small enough, is approximated by a diffusion process. If action-angle coordinates can be introduced only piece-wise, the limiting diffusion process

We illustrate the mathematical theory of entropy production in repeated quantum measurement processes developed in a previous work by studying examples of quantum instruments displaying various interesting phenomena and singularities. We emphasize the role of the thermodynamic formalism, and give many examples of quantum instruments whose resulting probability measures on the space of infinite sequences

Many integrable statistical mechanical models possess a fractional-spin conserved current. Such currents have been constructed by utilising quantum-group algebras and ideas from “discrete holomorphicity”. I find them naturally and much more generally using a braided tensor category, a topological structure arising in knot invariants, anyons and conformal field theory. I derive a simple constraint on

We study the behaviour of an interacting particle system, related to the Bak–Sneppen model and Jante’s law process defined in Kennerberg and Volkov (Adv Appl Probab 50:414–439, 2018). Let \(N\ge 3\) vertices be placed on a circle, such that each vertex has exactly two neighbours. To each vertex assign a real number, called fitness (we use this term, as it is quite standard for Bak–Sneppen models).

We uncovered an error in 1 that claims the predictive rate-distortion function separates achievable from unachievable sensors.

The Goldstein-Taylor equations can be thought of as a simplified version of a BGK system, where the velocity variable is constricted to a discrete set of values. It is intimately related to turbulent fluid motion and the telegrapher’s equation. A detailed understanding of the large time behaviour of the solutions to these equations has been mostly achieved in the case where the relaxation function

We study Eigen’s model of quasi-species (Eigen in Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften 58(10):465, 1971), characterized by sequences that replicate with a specified fitness and mutate independently at single sites. The evolution of the population vector in time is then closely related to that of quantum spins in imaginary time. We employ multiple

In this article we study the scaling limit of the interface model on \({{\,\mathrm{{\mathbb {Z}}}\,}}^d\) where the Hamiltonian is given by a mixed gradient and Laplacian interaction. We show that in any dimension the scaling limit is given by the Gaussian free field. We discuss the appropriate spaces in which the convergence takes place. While in infinite volume the proof is based on Fourier analytic

We numerically study the relaxation dynamics and associated criticality of non-Brownian frictionless soft spheres below jamming in spatial dimensions \(d=2\), 3, 4, and 8, and in the mean-field Mari–Kurchan model. We discover non-trivial finite-size and volume fraction dependences of the relaxation time associated to the relaxation of unjammed packings. In particular, the relaxation time is shown to

In a recent paper (J Stat Phys 179:729–747, 2020) time evolution of the telegrapher’s equation subjected to a random velocity field was studied in the context of the effective medium approximation. In addition, the solution for the mean-value of the field was presented as a series expansion in Terwiel’s cumulants. Here we have proved that this expansion cuts if the random velocity field is emulated