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作者：Martinelli, Fabio; Toninelli, Cristina
作者单位：Roma Tre University; Centre National de la Recherche Scientifique (CNRS)
摘要：Recent years have seen a great deal of progress in our understanding of bootstrap percolation models, a particular class of monotone cellular automata. In the two-dimensional lattice Z(2), there is now a quite satisfactory understanding of their evolution starting from a random initial condition, with a strikingly beautiful universality picture for their critical behavior. Much less is known for their nonmonotone stochastic counterpart, namely kinetically constrained models (KCM). In KCM, each...
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作者：Bobkov, S. G.; Chistyakov, G. P.; Goerzet, F.
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Bielefeld
摘要：We explore properties of the chi(2) and Renyi distances to the normal law and in particular propose necessary and sufficient conditions under which these distances tend to zero in the central limit theorem (with exact rates with respect to the increasing number of summands).
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作者：Shao, Qi-Man; Zhang, Zhuo-Song
作者单位：Chinese University of Hong Kong
摘要：An exchangeable pair approach is commonly taken in the normal and nonnormal approximation using Stein's method. It has been successfully used to identify the limiting distribution and provide an error of approximation. However, when the difference of the exchangeable pair is not bounded by a small deterministic constant, the error bound is often not optimal. In this paper, using the exchangeable pair approach of Stein's method, a new Berry-Esseen bound for an arbitrary random variable is estab...
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作者：Butkovsky, Oleg; Mytnik, Leonid
作者单位：Technion Israel Institute of Technology
摘要：Motivated by the regularization by noise phenomenon for SDEs, we prove existence and uniqueness of the flow of solutions for the non-Lipschitz stochastic heat equation partial derivative u/partial derivative t = 1/2 partial derivative(2)u/partial derivative z(2) + b(u(t,z)) + <(W)single over dot>(t,z), where <(W)single over dot> is a space-time white noise on R+ x R and b is a bounded measurable function on R. As a byproduct of our proof, we also establish the so-called path-by-path uniqueness...
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作者：Dalang, Robert C.; Khoshnevisan, Davar; Zhang, Tusheng
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Utah System of Higher Education; University of Utah; University of Manchester
摘要：Let xi(t, x) denote space-time white noise and consider a reaction-diffusion equation of the form <(u) over dot>(t, x) = 1/2u ''(t, x) + b(u(t, x)) + sigma(u(t,x))xi(t,x) on R+ x [0, 1], with homogeneous Dirichlet boundary conditions and suitable initial data, in the case that there exists epsilon > 0 such that vertical bar b(z)vertical bar >= vertical bar z vertical bar (log vertical bar z vertical bar)(1+epsilon) for all sufficiently-large values of vertical bar z vertical bar. When sigma eq...
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作者：Cass, Thomas; Lim, Nengli
作者单位：Imperial College London; Singapore University of Technology & Design
摘要：Given a Gaussian process X, its canonical geometric rough path lift X, and a solution Y to the rough differential equation (RDE) dY(t) = V (Y-t) circle dX(t), we present a closed-form correction formula for integral Y circle dX - integral Y dX, that is, the difference between the rough and Skorohod integrals of Y with respect to X. When X is standard Brownian motion, we recover the classical Stratonovich-to-Ito conversion formula, which we generalize to Gaussian rough paths with finite p-varia...
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作者：Ghoussoub, Nassif; Kim, Young-Heon; Lim, Tongseok
作者单位：University of British Columbia; Korea Institute for Advanced Study (KIAS); ShanghaiTech University
摘要：Given two probability measures mu and nu in convex order on R-d, we study the profile of one-step martingale plans pi on R-d x R-d that optimize the expected value of the modulus of their increment among all martingales having mu and nu as marginals. While there is a great deal of results for the real line (i.e., when d = 1), much less is known in the richer and more delicate higher-dimensional case that we tackle in this paper. We show that many structural results can be obtained, provided th...
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作者：Tikhomirov, Konstantin; Youssef, Pierre
作者单位：Princeton University; Universite Paris Cite
摘要：For any alpha is an element of (0,1) and any n(alpha) <= d <= n/2, we show that lambda(G) <= C-alpha root d with probability at least 1 - 1/n, where G is the uniform random undirected d-regular graph on n vertices, lambda(G) denotes its second largest eigenvalue (in absolute value) and C-alpha is a constant depending only on alpha. Combined with earlier results in this direction covering the case of sparse random graphs, this completely settles the problem of estimating the magnitude of lambda...
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作者：Chen, Zhen-Qing; Lou, Shuwen
作者单位：University of Washington; University of Washington Seattle; University of Toronto
摘要：In this paper, we introduce and study Brownian motion on a class of state spaces with varying dimension. Starting with a concrete case of such state spaces that models a big square with a flag pole, we construct a Brownian motion on it and study how heat propagates on such a space. We derive sharp two-sided global estimates on its transition density function (also called heat kernel). These two-sided estimates are of Gaussian type, but the measure on the underlying state space does not satisfy...
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作者：Funaki, Tadahisa; Yokoyama, Satoshi
作者单位：University of Tokyo; Waseda University
摘要：This paper studies the sharp interface limit for a mass conserving Allen-Cahn equation, added an external noise and derives a stochastically perturbed mass conserving mean curvature flow in the limit. The stochastic term destroys the precise conservation law, instead the total mass changes like a Brownian motion in time. For our equation, the comparison argument does not work, so that to study the limit we adopt the asymptotic expansion method, which extends that for deterministic equations us...
