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New results for the random nearest neighbor tree Probab Theory Relat Fields (IF 2.0) Pub Date : 2024-03-17 Lyuben Lichev, Dieter Mitsche
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Spectral gap estimates for mixed p-spin models at high temperature Probab Theory Relat Fields (IF 2.0) Pub Date : 2024-03-17 Arka Adhikari, Christian Brennecke, Changji Xu, Horng-Tzer Yau
We consider general mixed p-spin mean field spin glass models and provide a method to prove that the spectral gap of the Dirichlet form associated with the Gibbs measure is of order one at sufficiently high temperature. Our proof is based on an iteration scheme relating the spectral gap of the N-spin system to that of suitably conditioned subsystems.
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A multivariate extension of the Erdős–Taylor theorem Probab Theory Relat Fields (IF 2.0) Pub Date : 2024-03-15 Dimitris Lygkonis, Nikos Zygouras
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Stationary measures for stochastic differential equations with degenerate damping Probab Theory Relat Fields (IF 2.0) Pub Date : 2024-03-12 Jacob Bedrossian, Kyle Liss
A variety of physical phenomena involve the nonlinear transfer of energy from weakly damped modes subjected to external forcing to other modes which are more heavily damped. In this work we explore this in (finite-dimensional) stochastic differential equations in \({\mathbb {R}}^n\) with a quadratic, conservative nonlinearity B(x, x) and a linear damping term—Ax which is degenerate in the sense that
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Instantaneous everywhere-blowup of parabolic SPDEs Probab Theory Relat Fields (IF 2.0) Pub Date : 2024-03-05
Abstract We consider the following stochastic heat equation $$\begin{aligned} \partial _t u(t,x) = \tfrac{1}{2} \partial ^2_x u(t,x) + b(u(t,x)) + \sigma (u(t,x)) {\dot{W}}(t,x), \end{aligned}$$ defined for \((t,x)\in (0,\infty )\times {\mathbb {R}}\) , where \({\dot{W}}\) denotes space-time white noise. The function \(\sigma \) is assumed to be positive, bounded, globally Lipschitz, and bounded uniformly
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Heat kernel for reflected diffusion and extension property on uniform domains Probab Theory Relat Fields (IF 2.0) Pub Date : 2024-03-05 Mathav Murugan
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Mixing time of random walk on dynamical random cluster Probab Theory Relat Fields (IF 2.0) Pub Date : 2024-02-28 Andrea Lelli, Alexandre Stauffer
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Weak semiconvexity estimates for Schrödinger potentials and logarithmic Sobolev inequality for Schrödinger bridges Probab Theory Relat Fields (IF 2.0) Pub Date : 2024-02-28 Giovanni Conforti
We investigate the quadratic Schrödinger bridge problem, a.k.a. Entropic Optimal Transport problem, and obtain weak semiconvexity and semiconcavity bounds on Schrödinger potentials under mild assumptions on the marginals that are substantially weaker than log-concavity. We deduce from these estimates that Schrödinger bridges satisfy a logarithmic Sobolev inequality on the product space. Our proof strategy
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Strong posterior contraction rates via Wasserstein dynamics Probab Theory Relat Fields (IF 2.0) Pub Date : 2024-02-23 Emanuele Dolera, Stefano Favaro, Edoardo Mainini
In Bayesian statistics, posterior contraction rates (PCRs) quantify the speed at which the posterior distribution concentrates on arbitrarily small neighborhoods of a true model, in a suitable way, as the sample size goes to infinity. In this paper, we develop a new approach to PCRs, with respect to strong norm distances on parameter spaces of functions. Critical to our approach is the combination
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Geometry of the minimal spanning tree in the heavy-tailed regime: new universality classes Probab Theory Relat Fields (IF 2.0) Pub Date : 2024-02-17 Shankar Bhamidi, Sanchayan Sen
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The critical variational setting for stochastic evolution equations Probab Theory Relat Fields (IF 2.0) Pub Date : 2024-02-02 Antonio Agresti, Mark Veraar
In this paper we introduce the critical variational setting for parabolic stochastic evolution equations of quasi- or semi-linear type. Our results improve many of the abstract results in the classical variational setting. In particular, we are able to replace the usual weak or local monotonicity condition by a more flexible local Lipschitz condition. Moreover, the usual growth conditions on the multiplicative
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Geometric bounds on the fastest mixing Markov chain Probab Theory Relat Fields (IF 2.0) Pub Date : 2024-01-30 Sam Olesker-Taylor, Luca Zanetti
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Tractability from overparametrization: the example of the negative perceptron Probab Theory Relat Fields (IF 2.0) Pub Date : 2024-01-22 Andrea Montanari, Yiqiao Zhong, Kangjie Zhou
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W-entropy and Langevin deformation on Wasserstein space over Riemannian manifolds Probab Theory Relat Fields (IF 2.0) Pub Date : 2024-01-16 Songzi Li, Xiang-Dong Li
We prove the Perelman type W-entropy formula for the geodesic flow on the \(L^2\)-Wasserstein space over a complete Riemannian manifold equipped with Otto’s infinite dimensional Riemannian metric. To better understand the similarity between the W-entropy formula for the geodesic flow on the Wasserstein space and the W-entropy formula for the heat flow of the Witten Laplacian on the underlying manifold
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Eve, Adam and the preferential attachment tree Probab Theory Relat Fields (IF 2.0) Pub Date : 2024-01-12 Alice Contat, Nicolas Curien, Perrine Lacroix, Etienne Lasalle, Vincent Rivoirard
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Superconcentration for minimal surfaces in first passage percolation and disordered Ising ferromagnets Probab Theory Relat Fields (IF 2.0) Pub Date : 2024-01-05 Barbara Dembin, Christophe Garban
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On the Wiener chaos expansion of the signature of a Gaussian process Probab Theory Relat Fields (IF 2.0) Pub Date : 2024-01-04 Thomas Cass, Emilio Ferrucci
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Annealed quantitative estimates for the quadratic 2D-discrete random matching problem Probab Theory Relat Fields (IF 2.0) Pub Date : 2024-01-04 Nicolas Clozeau, Francesco Mattesini
We study a random matching problem on closed compact 2-dimensional Riemannian manifolds (with respect to the squared Riemannian distance), with samples of random points whose common law is absolutely continuous with respect to the volume measure with strictly positive and bounded density. We show that given two sequences of numbers n and \(m=m(n)\) of points, asymptotically equivalent as n goes to
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Anomalous diffusion limit for a kinetic equation with a thermostatted interface Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-12-29
Abstract We consider the limit of solutions of scaled linear kinetic equations with a reflection-transmission-killing condition at the interface. Both the coefficient describing the probability of killing and the scattering kernel degenerate. We prove that the long-time, large-space limit is the unique solution of a version of the fractional in space heat equation that corresponds to the Kolmogorov
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Sums of GUE matrices and concentration of hives from correlation decay of eigengaps Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-12-28 Hariharan Narayanan, Scott Sheffield, Terence Tao
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Symmetric cooperative motion in one dimension Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-12-09 Louigi Addario-Berry, Erin Beckman, Jessica Lin
We explore the relationship between recursive distributional equations and convergence results for finite difference schemes of parabolic partial differential equations (PDEs). We focus on a family of random processes called symmetric cooperative motions, which generalize the symmetric simple random walk and the symmetric hipster random walk introduced in Addario-Berry et al. (Probab Theory Related
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Fleming–Viot couples live forever Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-12-09 Mateusz Kwaśnicki
We prove a non-extinction result for Fleming–Viot-type systems of two particles with dynamics described by an arbitrary symmetric Hunt process under the assumption that the reference measure is finite. Additionally, we describe an invariant measure for the system, we discuss its ergodicity, and we prove that the reference measure is a stationary measure for the embedded Markov chain of positions of
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On the ergodicity of interacting particle systems under number rigidity Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-12-02 Kohei Suzuki
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Half-space depth of log-concave probability measures Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-11-29 Silouanos Brazitikos, Apostolos Giannopoulos, Minas Pafis
Given a probability measure \(\mu \) on \({{\mathbb {R}}}^n\), Tukey’s half-space depth is defined for any \(x\in {{\mathbb {R}}}^n\) by \(\varphi _{\mu }(x)=\inf \{\mu (H):H\in {{{\mathcal {H}}}}(x)\}\), where \(\mathcal{H}(x)\) is the set of all half-spaces H of \({{\mathbb {R}}}^n\) containing x. We show that if \(\mu \) is a non-degenerate log-concave probability measure on \({{\mathbb {R}}}^n\)
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Edge statistics for lozenge tilings of polygons, I: concentration of height function on strip domains Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-11-14 Jiaoyang Huang
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Harnack inequality and one-endedness of UST on reversible random graphs Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-11-08 Nathanaël Berestycki, Diederik van Engelenburg
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Optimal transport methods for combinatorial optimization over two random point sets Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-11-07 Michael Goldman, Dario Trevisan
We investigate the minimum cost of a wide class of combinatorial optimization problems over random bipartite geometric graphs in \(\mathbb {R}^d\) where the edge cost between two points is given by a pth power of their Euclidean distance. This includes e.g. the travelling salesperson problem and the bounded degree minimum spanning tree. We establish in particular almost sure convergence, as n grows
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On the lack of Gaussian tail for rough line integrals along fractional Brownian paths Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-10-30 H. Boedihardjo, X. Geng
We show that the tail probability of the rough line integral \(\int _{0}^{1}\phi (X_{t})dY_{t}\), where (X, Y) is a 2D fractional Brownian motion with Hurst parameter \(H\in (1/4,1/2)\) and \(\phi \) is a \(C_{b}^{\infty }\)-function satisfying a mild non-degeneracy condition on its derivative, cannot decay faster than a \(\gamma \)-Weibull tail with any exponent \(\gamma >2H+1\). In particular, this
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Quantitative stability of barycenters in the Wasserstein space Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-10-25 Guillaume Carlier, Alex Delalande, Quentin Mérigot
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Slightly supercritical percolation on nonamenable graphs II: growth and isoperimetry of infinite clusters Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-10-17 Tom Hutchcroft
We study the growth and isoperimetry of infinite clusters in slightly supercritical Bernoulli bond percolation on transitive nonamenable graphs under the \(L^2\) boundedness condition (\(p_c
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On the pitchfork bifurcation for the Chafee–Infante equation with additive noise Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-10-05 Alex Blumenthal, Maximilian Engel, Alexandra Neamţu
We investigate pitchfork bifurcations for a stochastic reaction diffusion equation perturbed by an infinite-dimensional Wiener process. It is well-known that the random attractor is a singleton, independently of the value of the bifurcation parameter; this phenomenon is often referred to as the “destruction” of the bifurcation by the noise. Analogous to the results of Callaway et al. (AIHP Prob Stat
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Global existence and non-uniqueness of 3D Euler equations perturbed by transport noise Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-10-03 Martina Hofmanová, Theresa Lange, Umberto Pappalettera
We construct Hölder continuous, global-in-time probabilistically strong solutions to 3D Euler equations perturbed by Stratonovich transport noise. Kinetic energy of the solutions can be prescribed a priori up to a stopping time, that can be chosen arbitrarily large with high probability. We also prove that there exist infinitely many Hölder continuous initial conditions leading to non-uniqueness of
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Mesoscopic central limit theorem for non-Hermitian random matrices Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-09-28 Giorgio Cipolloni, László Erdős, Dominik Schröder
We prove that the mesoscopic linear statistics \(\sum _i f(n^a(\sigma _i-z_0))\) of the eigenvalues \(\{\sigma _i\}_i\) of large \(n\times n\) non-Hermitian random matrices with complex centred i.i.d. entries are asymptotically Gaussian for any \(H^{2}_0\)-functions \(f\) around any point \(z_0\) in the bulk of the spectrum on any mesoscopic scale \(0
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The random walk on upper triangular matrices over $$\mathbb {Z}/m \mathbb {Z}$$ Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-09-27 Evita Nestoridi, Allan Sly
We study a natural random walk on the \(n \times n\) uni-upper triangular matrices, with entries in \(\mathbb {Z}/m \mathbb {Z}\), generated by steps which add or subtract a uniformly random row to the row above. We show that the mixing time of this random walk is \(O(m^2n \log n+ n^2 m^{o(1)})\). This answers a question of Stong and of Arias-Castro, Diaconis, and Stanley.
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Local law and rigidity for unitary Brownian motion Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-09-25 Arka Adhikari, Benjamin Landon
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Stationary local random countable sets over the Wiener noise Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-09-26 Matija Vidmar, Jon Warren
The times of Brownian local minima, maxima and their union are three distinct examples of local, stationary, dense, random countable sets associated with classical Wiener noise. Being local means, roughly, determined by the local behavior of the sample paths of the Brownian motion, and stationary means invariant relative to the Lévy shifts of the sample paths. We answer to the affirmative Tsirelson’s
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Long lines in subsets of large measure in high dimension Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-09-22 Dor Elboim, Bo’az Klartag
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An asymptotic formula for the variance of the number of zeroes of a stationary Gaussian process Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-09-23 Eran Assaf, Jeremiah Buckley, Naomi Feldheim
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Extremal singular values of random matrix products and Brownian motion on $$\textsf {GL} (N,\mathbb {C})$$ Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-09-20 Andrew Ahn
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Hamilton–Jacobi scaling limits of Pareto peeling in 2D Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-09-18 Ahmed Bou-Rabee, Peter S. Morfe
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Upper tail of the spectral radius of sparse Erdös–Rényi graphs Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-09-15 Anirban Basak
We consider an Erdös–Rényi graph \(\mathbb {G}(n,p)\) on n vertices with edge probability p such that $$\begin{aligned} \sqrt{\frac{\log n}{\log \log n}} \ll np \leqslant n^{1/2-o(1)}, \end{aligned}$$(†) and derive the upper tail large deviations of \(\lambda (\mathbb {G}(n,p))\), the largest eigenvalue of its adjacency matrix. Within this regime we show that, for \(p \gg n^{-2/3}\) the \(\log \)-probability
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Limit theory for the first layers of the random convex hull peeling in the unit ball Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-09-05 Pierre Calka, Gauthier Quilan
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Marginal dynamics of interacting diffusions on unimodular Galton–Watson trees Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-08-29 Daniel Lacker, Kavita Ramanan, Ruoyu Wu
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There is no stationary cyclically monotone Poisson matching in 2d Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-08-29 Martin Huesmann, Francesco Mattesini, Felix Otto
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Convergence of genealogies through spinal decomposition with an application to population genetics Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-08-18 Félix Foutel-Rodier, Emmanuel Schertzer
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Correction to: Asymptotic moments of spatial branching processes Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-07-21 Isaac Gonzalez, Emma Horton, Andreas E. Kyprianou
Abstract We correct the statements of the non-critical convergence theorems in Gonzalez et al. (Probab Theory Rel Fields, 2022), principally correcting the recursive constants that appear in the limits.
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Three-point correlation functions in the $$\mathfrak {sl}_3$$ Toda theory I: reflection coefficients Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-07-13 Baptiste Cerclé
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Spread of infections in a heterogeneous moving population Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-07-13 Duncan Dauvergne, Allan Sly
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From robust tests to Bayes-like posterior distributions Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-07-13 Yannick Baraud
In the Bayes paradigm, given a loss function and an n-sample, we present the construction of a new type of posterior distribution, that extends the classical Bayes one. The loss functions we have in mind are either those derived from the total variation and Hellinger distances or some \({\mathbb {L}}_{j}\)-ones for \(j>1\). We prove that, with a probability close to one, this new posterior distribution
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Correction to: Quenched large deviation principle for words in a letter sequence Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-07-03 Matthias Birkner, Andreas Greven, Frank den Hollander
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Propagation of chaos for maxima of particle systems with mean-field drift interaction Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-06-23 Nikolaos Kolliopoulos, Martin Larsson, Zeyu Zhang
We study the asymptotic behavior of the normalized maxima of real-valued diffusive particles with mean-field drift interaction. Our main result establishes propagation of chaos: in the large population limit, the normalized maxima behave as those arising in an i.i.d. system where each particle follows the associated McKean–Vlasov limiting dynamics. Because the maximum depends on all particles, our
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Central limit type theorem and large deviation principle for multi-scale McKean–Vlasov SDEs Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-06-17 Wei Hong, Shihu Li, Wei Liu, Xiaobin Sun
The main aim of this work is to study the asymptotic behavior for multi-scale McKean–Vlasov stochastic dynamical systems. Firstly, we obtain a central limit type theorem, i.e. the deviation between the slow component \(X^{\varepsilon }\) and the solution \({\bar{X}}\) of the averaged equation converges weakly to a limiting process. More precisely, \(\frac{X^{\varepsilon }-{\bar{X}}}{\sqrt{\varepsilon
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The planted matching problem: sharp threshold and infinite-order phase transition Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-06-06 Jian Ding, Yihong Wu, Jiaming Xu, Dana Yang
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Malliavin calculus and densities for singular stochastic partial differential equations Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-05-24 Philipp Schönbauer
We study Malliavin differentiability of solutions to sub-critical singular parabolic stochastic partial differential equations (SPDEs) and we prove the existence of densities for a class of singular SPDEs. Both of these results are implemented in the setting of regularity structures. For this we construct renormalized models in situations where some of the driving noises are replaced by deterministic
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Anticoncentration and Berry–Esseen bounds for random tensors Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-05-22 Pandelis Dodos, Konstantinos Tyros
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Free boundary dimers: random walk representation and scaling limit Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-05-16 Nathanaël Berestycki, Marcin Lis, Wei Qian
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Matrix Whittaker processes Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-05-14 Jonas Arista, Elia Bisi, Neil O’Connell
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On the $$\Phi $$ -stability and related conjectures Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-05-12 Lei Yu
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Stefan problem with surface tension: global existence of physical solutions under radial symmetry Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-05-08 Sergey Nadtochiy, Mykhaylo Shkolnikov
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The free energy of spherical pure p-spin models: computation from the TAP approach Probab Theory Relat Fields (IF 2.0) Pub Date : 2023-05-03 Eliran Subag
We compute the free energy at all temperatures for the spherical pure p-spin models from the generalized Thouless–Anderson–Palmer representation. This is the first example of a mixed p-spin model for which the free energy is computed in the whole replica symmetry breaking phase, without appealing to the famous Parisi formula.