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作者：Prevost, Alexis; Rodriguez, Pierre-Francois; Sousi, Perla
作者单位：University of Bonn; Imperial College London; University of Cambridge
摘要：Let X be a random walk on the torus of side length N in dimension d >= 3 with uniform starting point, and t(cov) be the expected value of its cover time, which is the first time that X has visited every vertex of the torus at least once. For alpha> 0, the set L-alpha of alpha-late points consists of those points not visited by X at time alpha t(cov). We prove the existence of a value alpha & lowast; is an element of ( 1/2 , 1) across which L-alpha trivialises as follows: for all alpha>alpha & ...
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作者：Sojmark, Andreas; Wunderlich, Fabrice
作者单位：University of London; London School Economics & Political Science; University of Oxford
摘要：We provide criteria for It & ocirc; integration to behave continuously with respect to Skorokhod's J1 and M1 topologies, when the integrands and integrators converge weakly or in probability. The results are novel in the M1 setting and unify existing theories in the J1 case. Beyond sufficient criteria, we present an example of uniformly convergent martingale integrators for which the continuity breaks down. Moreover, we show that, for families of local martingales, M1 tightness in fact implies...
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作者：Rhee, Chang-Han; Ryu, Jeeho; Seo, Insuk
作者单位：Northwestern University; Seoul National University (SNU); Seoul National University (SNU); Seoul National University (SNU); Korea Institute for Advanced Study (KIAS)
摘要：Kesten's stochastic recurrent equation is a classical subject of research in probability theory and its applications. Recently, it has garnered attention as a model for stochastic gradient descent with a quadratic objective function and the emergence of heavy-tailed dynamics in machine learning. This context calls for analysis of its asymptotic behavior under both negative and positive Lyapunov exponents. This paper studies the exit times of the Kesten's stochastic recurrence equation in both ...
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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：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 ...
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作者：Funaki, Tadahisa
摘要：We consider the Glauber-Kawasaki dynamics on a d-dimensional periodic lattice of size N, that is, a stochastic time evolution of particles performing random walks with interaction subject to the exclusion rule (Kawasaki part), in general, of non-gradient type, together with the effect of the creation and annihilation of particles (Glauber part) whose rates are set to favor two levels of particle density, called sparse and dense. We then study the limit of our dynamics under the hydrodynamic sp...
