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作者：Ren, Zhenjie; Wang, Songbo
作者单位：Universite Cote d'Azur
摘要：We investigate Gibbs measures for diffusive particles interacting through a two-body mean field energy. By identifying a gradient structure for the conditional law, we derive sharp bounds on the size of chaos, providing a quantitative characterization of particle independence. To handle interaction forces that are unbounded at infinity, we study the concentration of measure phenomenon for Gibbs measures via a defective Talagrand inequality, which may hold independent interest. Our approach pro...
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作者：Bernou, Armand; Duerinckx, Mitia
作者单位：Universite Lyon 1; Universite Libre de Bruxelles
摘要：We consider a system of N classical Brownian particles interacting via a smooth long-range potential in the mean-field regime, and we analyze the propagation of chaos in form of uniform-in-time estimates with optimal N-dependence on many-particle correlation functions. Our results cover both the kinetic Langevin setting and the corresponding overdamped Brownian dynamics. The approach is mainly based on so-called Lions expansions, which we combine with new diagrammatic tools to capture many-par...
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作者：Angel, Omer; Riva, Daniel de la; Hermon, Jonathan; Shi, Yuliang
作者单位：University of British Columbia
摘要：We consider a slight modification of the frog model. For a given graph, each vertex has Poisson(lambda) particles (or frogs). At time zero, only the particles at the origin are active, and all the other particles are sleeping. Each active particle performs an independent, continuous-time simple random walk up to a fixed lifetime t, after which the particle dies and is removed from the system. Once an active frog jumps to a vertex, it activates all of its particles. The survival of active parti...
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作者：Ben Arous, Gerard; Gerbelot, Cedric; Piccolo, Vanessa
作者单位：New York University; Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We study nonconvex optimization in high dimensions through Langevin dynamics, focusing on the multi-spiked tensor PCA problem. In this tensor estimation model, the goal is to recover a finite number of hidden signal vectors, or spikes, from noisy Gaussian tensor observations using maximum likelihood estimation. We characterize the number of samples required for Langevin dynamics to efficiently recover the spikes and identify the separation conditions on the signal- to-noise ratios (SNRs) neede...
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作者：Cannizzaro, Giuseppe; Klose, Tom; Moulard, Quentin
作者单位：University of Warwick; University of Oxford; Technische Universitat Wien
摘要：We study the large-scale behaviour of a class of driven diffusive systems modelled by a Stochastic Partial Differential Equation, the Stochastic Burgers Equation (SBE) with general nonlinearity, at the critical dimension and in infinite volume. Our main result shows that, under a logarithmically superdiffusive space-time scaling, it is given by the same explicit Gaussian Fixed point obtained in [G. Cannizzaro, Q. Moulard, & F. Toninelli, 2025] for the quadratic SBE, but with suitably renormali...
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作者：Chhaibi, Reda; Defosseux, Manon
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
摘要：The process (integral 0te2bs-btdst >= 0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\int _0<^>t e<^>{2b_s-b_t}\, ds\;\ t\ge 0)$$\end{document}, where b is a real Brownian motion, is known as the geometric 2M-X Matsumoto-Yor process. Remarkably, it enjoys the Markov property. We provide a generalization of this...
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作者：Busani, Ofer
作者单位：University of Edinburgh
摘要：It is believed that for metric-like models in the KPZ class the following property holds: with probability one, starting from any point, there are at most two semi-infinite geodesics with the same direction that do not coalesce. Until now, such a result was only proved for one model - exponential LPP (Coupier, D., in Electron. Commun. Probab. 16, 517-527, 2011) using its inherent connection to the totally asymmetric exclusion process. We prove that the above property holds for the directed lan...
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作者：Milman, Emanuel
作者单位：Technion Israel Institute of Technology
摘要：We give a simple alternative proof of Royen's Gaussian Correlation inequality by using (a slightly generalized version of) Nakamura-Tsuji's symmetric inverse Brascamp-Lieb inequality for even log-concave functions. We explain that this inverse inequality is in a certain sense a dual counterpart to the forward inequality of Bennett-Carbery-Christ-Tao and Valdimarsson, and that the log-concavity assumption therein cannot be omitted in general.
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作者：Melbourne, James; Nayar, Piotr; Roberto, Cyril
作者单位：CIMAT - Centro de Investigacion en Matematicas; University of Warsaw; Centre National de la Recherche Scientifique (CNRS)
摘要：We show that for log-concave real random variables with fixed variance the Shannon differential entropy is minimized for an exponential random variable, answering a 2010 question of Bobkov and Madiman [1]. This gives a sharp reversal of the celebrated entropy maximization theorem due to Boltzmann, in the log-concave case. We apply this result to derive upper bounds on capacities of additive noise channels with log-concave noise. We also improve constants in the reverse entropy power inequaliti...
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作者：Menshikov, Mikhail; Popov, Serguei; Wade, Andrew
作者单位：Durham University; Universidade do Porto
摘要：We study semi-infinite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which suppresses jumps that would lead to more than one particle occupying any site. Under appropriate hypotheses on the jump rates (uniformly bounded rates is sufficient) and started from an initial condition that is a finite perturbation of the close-packed ...
