5期

最新文章

• DIFFUSIVE SCALING LIMIT OF THE BUSEMANN PROCESS IN LAST PASSAGE PERCOLATION AI翻译
  作者：Usani, Ofer
  作者单位：University of Edinburgh
  摘要：In exponential last passage percolation, we consider the rescaled Busemann process x bar right arrow N-(1/3) B-0,[xN2/3]e1(rho), x is an element of R, as a process parametrized by the scaled density rho = 1/2+ mu/4 N-1/3, and taking values in C(R). We show that these processes, as N -> infinity, have a right continuous left limit scaling limit G = (G(mu))(mu is an element of R), parametrized by mu and taking values in C(R). The limiting process G, which can be thought of as the Busemann proces...
• PATH-BY-PATH REGULARISATION THROUGH MULTIPLICATIVE NOISE IN ROUGH, YOUNG, AND ORDINARY DIFFERENTIAL EQUATIONS AI翻译
  作者：Dareiotis, Konstantinos; Gerencser, Mate
  作者单位：University of Leeds; Technische Universitat Wien
  摘要：Differential equations perturbed by multiplicative fractional Brownian motions are considered. Depending on the value of the Hurst parameter H, the resulting equation is pathwise viewed as an ODE, YDE, or RDE. In all three regimes, we show regularisation by noise phenomena by proving the strongest kind of well-posedness with irregular drift: strong existence and path-by-path uniqueness. In the Young and smooth regime H > 1/2, the condition on the drift coefficient is optimal in the sense that ...
• FRACTIONAL DIFFUSION LIMIT FOR A KINETIC FOKKER-PLANCK EQUATION WITH DIFFUSIVE BOUNDARY CONDITIONS IN THE HALF-LINE AI翻译
  作者：Bethencourt, Loic
  作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Sorbonne Universite
  摘要：We consider a particle with position (X-t)(t >= 0) living in R+, whose velocity (V-t)(t >= 0) is a positive recurrent diffusion with heavy-tailed invariant distribution when the particle lives in (0, infinity). When it hits the boundary x = 0, the particle restarts with a random strictly positive velocity. We show that the properly rescaled position process converges weakly to a stable process reflected on its infimum. From a P.D.E. point of view, the time-marginals of (X-t, V-t)(t >= 0) solve...
• DYNAMICAL LOOP EQUATION AI翻译
  作者：Gorin, Vadim; Huang, Jiaoyang
  作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley; University of Pennsylvania
  摘要：We introduce dynamical versions of loop (or Dyson-Schwinger) equations for large families of two-dimensional interacting particle systems, including Dyson Brownian motion, Nonintersecting Bernoulli/Poisson random walks, beta -corners processes, uniform and Jack-deformed measures on Gelfand-Tsetlin patterns, Macdonald processes, and (q, kappa)-distributions on lozenge tilings. Under technical assumptions we show that the dynamical loop equations lead to Gaussian field type fluctuations. As an a...
• LYAPUNOV EXPONENTS AND SYNCHRONISATION BY NOISE FOR SYSTEMS OF SPDES AI翻译
  作者：Gess, Benjamin; Tsatsoulis, Pavlos
  作者单位：University of Bielefeld
  摘要：Quantitative estimates for the top Lyapunov exponents for systems of stochastic reaction-diffusion equations are proven. The treatment includes reaction potentials with degenerate minima. The proof relies on an asymptotic expansion of the invariant measure, with careful control on the resulting error terms. As a consequence of these estimates, synchronisation by noise is deduced for systems of stochastic reaction-diffusion equations for the first time.
• THE CRITICAL DENSITY FOR ACTIVATED RANDOM WALKS IS ALWAYS LESS THAN 1 AI翻译
  作者：Asselah, Amine; Forien, Nicolas; Gaudilliere, Alexandre
  作者单位：Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Sapienza University Rome; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
  摘要：Activated Random Walks, , on Zd d for any d >= 1, is an interacting particle system, where particles can be in either of two states: active or frozen. Each active particle performs a continuous-time simple random walk during an exponential time of parameter lambda , after which it stays still in the frozen state, until another active particle shares its location, and turns it instantaneously back into activity. This model is known to have a phase transition, and we show that the critical densi...
• CAPACITY OF THE RANGE OF RANDOM WALK: THE LAW OF THE ITERATED LOGARITHM AI翻译
  作者：Dembo, Amir; Okada, Izumi
  作者单位：Stanford University; Chiba University
  摘要：We establish both the lim sup and the lim inf law of the iterated logarithm (LIL) for the capacity of the range of a simple random walk in any dimension d >= 3. While for d >= 4, the order of growth in n of such LIL at dimension d matches that for the volume of the random walk range in dimension d - 2, somewhat surprisingly this correspondence breaks down for the capacity of the range at d = 3. We further establish such LIL for the Brownian capacity of a three-dimensional Brownian sample path ...
• A LARGE DEVIATION INEQUALITY FOR THE RANK OF A RANDOM MATRIX AI翻译
  作者：Rudelson, Mark
  作者单位：University of Michigan System; University of Michigan
  摘要：Let A be an nxn x n random matrix with independent identically distributed nonconstant sub-Gaussian entries. Then for any k <= c ,J n , rank (A) >= n - k with probability at least 1 - exp ( - c l kn) .