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作者：Hu, Yueyun; Shi, Zhan
作者单位：Universite Paris 13; Universite Paris Cite; Sorbonne Universite
摘要：We consider a recurrent random walk in a random environment on a regular tree. Under suitable general assumptions concerning the distribution of the environment, we show that the walk exhibits an unusually slow movement: the order of magnitude of the walk in the first n steps is (log n)(3).
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作者：Debussche, Arnaud; Zambotti, Lorenzo
作者单位：Universite Paris Cite; Sorbonne Universite
摘要：We consider a stochastic partial differential equation with reflection at 0 and with the constraint of conservation of the space average. The equation is driven by the derivative in space of a space-time white noise and contains a double Laplacian in the drift. Due to the lack of the maximum principle for the double Laplacian, the standard techniques based on the penalization method do not yield existence of a solution. We propose a method based on infinite dimensional integration by parts for...
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作者：Hairer, M.; Ohashi, A.
作者单位：University of Warwick; Universidade Estadual de Campinas
摘要：We develop a theory of ergodicity for a class of random dynamical systems where the driving noise is not white. The two main tools of our analysis are the strong Feller property and topological irreducibility, introduced in this work for a class of non-Markovian systems. They allow us to obtain a criteria for ergodicity which is similar in nature to the Doob-Khas'minskii theorem. The second part of this article shows how it is possible to apply these results to the case of stochastic different...
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作者：Berestycki, Julien; Berestycki, Nathanaeel; Schweinsberg, Jason
作者单位：Aix-Marseille Universite; University of California System; University of California San Diego; University of British Columbia
摘要：Coalescents with multiple collisions, also known as Lambda-coalescents, were introduced by Pitman and Sagitov in 1999. These processes describe the evolution of particles that undergo stochastic coagulation in such a way that several blocks can merge at the same time to form a single block. In the case that the measure A is the Beta(2-alpha, alpha) distribution, they are also known to describe the genealogies of large populations where a single individual can produce a large number of offsprin...
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作者：Marckert, Jean-Francois; Miermont, Gregory
作者单位：Universite de Bordeaux; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
摘要：Random planar maps are considered in the physics literature as the discrete counterpart of random surfaces. It is conjectured that properly rescaled random planar maps, when conditioned to have a large number of faces, should converge to a limiting surface whose law does not depend, up to scaling factors, on details of the class of maps that are sampled. Previous works on the topic, starting with Chassaing and Schaeffer, have shown that the radius of a random quadrangulation with n faces, that...
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作者：Darses, Sebastien; Nourdin, Ivan
作者单位：Universite Marie et Louis Pasteur; Universite Paris Cite; Sorbonne Universite
摘要：In this paper, we introduce some fundamental notions related to the so-called stochastic derivatives with respect to a given a-field Q. In our framework, we recall well-known results about Markov-Wiener diffusions. We then focus mainly on the case where X is a fractional diffusion and where 62 is the past, the future or the present of X. We treat some crucial examples and our main result is the existence of stochastic derivatives with respect to the present of X when X solves a stochastic diff...
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作者：Goldstein, Larry
作者单位：University of Southern California
摘要：The zero bias distribution W* of W, defined though the characterizing equation EW f (W) = sigma(2) Ef ''(W*) for all smooth functions f, exists for all W with mean zero and finite variance sigma(2). For W and W* defined on the same probability space, the L-1 distance between F, the distribution function of W with EW = 0 and Var(W) = 1, and the cumulative standard normal phi has the simple upper bound parallel to F - Phi parallel to(1) <= vertical bar W-* - W vertical bar This inequality is use...
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作者：Holmes, Mark; Perkins, Edwin
作者单位：Euratom; University of British Columbia
摘要：We prove a sufficient set of conditions for a sequence of finite measures on the space of cadlag measure-valued paths to converge to the canonical measure of super-Brownian motion in the sense of convergence of finite-dimensional distributions. The conditions are convergence of the Fourier transform of the r-point functions and perhaps convergence of the survival probabilities. These conditions have recently been shown to hold for a variety of statistical mechanical models, including critical ...
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作者：Pang, Huadong; Stroock, Daniel W.
作者单位：Massachusetts Institute of Technology (MIT)
摘要：In this paper we consider a one-dimensional diffusion equation on the interval [0, 1] satisfying non-Feller boundary conditions. As a consequence, the initial value Cauchy problem fails to preserve nonnegativity or boundedness. Nonetheless, probability theory plays an interesting role in our analysis and understanding of solutions to this equation.
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作者：Baik, Jinho; Suidan, Toufic M.
作者单位：University of Michigan System; University of Michigan; University of California System; University of California Santa Cruz
摘要：We consider nonintersecting random walks satisfying the condition that the increments have a finite moment generating function. We prove that in a certain limiting regime where the number of walks and the number of time steps grow to infinity, several limiting distributions of the walks at the mid-time behave as the eigenvalues of random Hermitian matrices as the dimension of the matrices grows to infinity.
