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作者：Evans, Steven N.
作者单位：University of California System; University of California Berkeley
摘要：We consider the asymptotic behavior as n -> infinity of the spectra of random matrices of the form 1/root n-1 (n-1)Sigma(k=1) Z(nk)rho(n) ((k, k + 1)), where for each n the random variables Z(nk) are i.i.d. standard Gaussian and the matrices rho(n) ((k, k + 1)) are obtained by applying an irreducible unitary representation rho(n) of the symmetric group on {1, 2,...,n} to the transposition (k, k + 1) that interchanges k and k + 1 [thus, rho(n) ((k, k + 1)) is both unitary and self-adjoint, with...
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作者：Kurt, Noemi
作者单位：University of Zurich
摘要：We consider the real-valued centered Gaussian field on the four-dimensional integer lattice, whose covariance matrix is given by the Green's function of the discrete Bilaplacian. This is interpreted as a model for a semi-flexible membrane. d = 4 is the critical dimension for this model. We discuss the effect of a hard wall on the membrane, via a multiscale analysis of the maximum of the field. We use analytic and probabilistic tools to describe the correlation structure of the field.
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作者：Last, Guenter; Thorisson, Hermann
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; University of Iceland
摘要：We introduce and study invariant (weighted) transport-kernels balancing stationary random measures on a locally compact Abelian group. The first main result is an associated fundamental invariance property of Palm measures, derived from a generalization of Neveu's exchange formula. The second main result is a simple sufficient and necessary criterion for the existence of balancing invariant transport-kernels. We then introduce (in a nonstationary setting) the concept of mass-stationarity with ...
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作者：Pinsky, Ross G.
作者单位：Technion Israel Institute of Technology
摘要：Let D not subset of R(d) be an unbounded domain and let B(t) be a Brownian motion in D with normal reflection at the boundary. We study the transcience/recurrence dichotomy, focusing mainly on domains of the form D = {(x,z) is an element of R(l+m) : vertical bar z vertical bar < H(vertical bar x vertical bar)}, where d = l + m and H is a sufficiently regular function. This class of domains includes various horn-shaped domains and generalized slab domains.
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作者：Fey, Anne; Meester, Ronald; Redig, Frank
作者单位：Vrije Universiteit Amsterdam; Leiden University; Leiden University - Excl LUMC
摘要：We study the sandpile model in infinite volume on Z(d). In particular, we are interested in the question whether or not initial configurations, chosen according to a stationary measure mu, are mu-almost surely stabilizable. We prove that stabilizability does not depend on the particular procedure of stabilization we adopt. In d = 1 and mu a product measure with density rho = 1 (the known critical value for stabilizability in d = 1) with a positive density of empty sites, we prove that mu is no...
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作者：Bramson, Maury; Zeitouni, Ofer
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Weizmann Institute of Science
摘要：In this paper we study the tightness of solutions for a family of recursion equations. These equations arise naturally in the study of random walks on tree-like structures. Examples include the maximal displacement of a branching random walk in one dimension and the cover time of a symmetric simple random walk on regular binary trees. Recursion equations associated with the distribution functions of these quantities have been used to establish weak laws of large numbers. Here, we use these rec...
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作者：Barbu, Viorel; Da Prato, Giuseppe; Roeckner, Michael
作者单位：Alexandru Ioan Cuza University; Scuola Normale Superiore di Pisa; University of Bielefeld; Purdue University System; Purdue University
摘要：This paper addresses the existence and uniqueness of strong solutions to stochasic porous media equations dX - Delta Psi(X)dt = B(X)dW(t) in bounded domains of R-d with Dirichlet boundary conditions. Here Psi is a maximal monotone graph in R x R (possibly multivalued) with the domain and range all of R. Compared with the existing literature on stochastic porous media equations, no growth condition on Psi is assumed and the diffusion coefficient Psi might be multivalued and discontinuous. The l...
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作者：Morris, Ben
作者单位：University of California System; University of California Davis
摘要：We prove a theorem that reduces bounding the mixing time of a card shuffle to verifying a condition that involves only pairs of cards, then We use it to obtain improved bounds for two previously studied models. E. Thorp introduced the following card shuffling model in 1973: Suppose the number of cards n is even. Cut the deck into two equal piles. Drop the first card from the left pile or from the right pile according to the outcome of a fair coin flip. Then drop from the other pile. Continue t...
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作者：Imkeller, Peter; Pavlyukevich, Ilya; Wetzel, Torsten
作者单位：Humboldt University of Berlin
摘要：We consider a dynamical system described by the differential equation (Y) over dot(t) = -U'(Y-t) with a unique stable point at the origin. We perturb the system by the Levy noise of intensity E to obtain the stochastic differential equation dX(t)(epsilon) = -U'(X-t-(epsilon)) dt + epsilon dL(t). The process L is a symmetric Levy process whose jump measure nu has exponentially light tails, nu([u, infinity)) similar to exp(- u(alpha)), alpha > 0, u -> infinity. We study the first exit problem fo...
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作者：Melbourne, Ian; Nicol, Matthew
作者单位：University of Surrey; University of Houston System; University of Houston
摘要：We prove an almost sure invariance principle (approximation by d-dimensional Brownian motion) for vector-valued Holder observables of large classes of nonuniformly hyperbolic dynamical systems. These systems include Axiom A diffeomorphisms and flows as well as systems modeled by Young towers with moderate tail decay rates. In particular, the position variable of the planar periodic Lorentz gas with finite horizon approximates a two-dimensional Brownian motion.
