Probability Theory and Related Fields

最新文章

• Approximation of Haar distributed matrices and limiting distributions of eigenvalues of Jacobi ensembles AI翻译
  作者：Jiang, Tiefeng
  作者单位：University of Minnesota System; University of Minnesota Twin Cities
  摘要：We develop a tool to approximate the entries of a large dimensional complex Jacobi ensemble with independent complex Gaussian random variables. Based on this and the author's earlier work in this direction, we obtain the Tracy-Widom law of the largest singular values of the Jacobi emsemble. Moreover, the circular law, the Marchenko-Pastur law, the central limit theorem, and the laws of large numbers for the spectral norms are also obtained.
• Branching-coalescing particle systems (vol 131, pg 376, 2005) AI翻译
  作者：Athreya, Siva R.; Swart, Jan M.
  作者单位：Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences; Indian Statistical Institute; Indian Statistical Institute Bangalore
• Invariant random graphs with iid degrees in a general geography AI翻译
  作者：Jonasson, Johan
  作者单位：Chalmers University of Technology; University of Gothenburg
  摘要：Let D be a non-negative integer-valued random variable and let G = (V, E) be an infinite transitive finite-degree graph. Continuing the work of Deijfen and Meester (Adv Appl Probab 38:287-298) and Deijfen and Jonasson (Electron Comm Probab 11: 336-346), we seek an Aut(G)-invariant random graph model with V as vertex set, iid degrees distributed as D and finite mean connections (i.e., the sum of the edge lengths in the graph metric of G of a given vertex has finite expectation). It is shown tha...
• The compound Poisson distribution and return times in dynamical systems AI翻译
  作者：Haydn, Nicolai; Vaienti, Sandro
  作者单位：University of Southern California; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; Aix-Marseille Universite; Aix-Marseille Universite; Universite de Toulon
  摘要：Previously it has been shown that some classes of mixing dynamical systems have limiting return times distributions that are almost everywhere Poissonian. Here we study the behaviour of return times at periodic points and show that the limiting distribution is a compound Poissonian distribution. We also derive error terms for the convergence to the limiting distribution. We also prove a very general theorem that can be used to establish compound Poisson distributions in many other settings.
• Laplace approximation for stochastic line integrals AI翻译
  作者：Kuwada, Kazumasa
  作者单位：Ochanomizu University
  摘要：We prove a precision of large deviation principle for current-valued processes such as shown in Bolthausen et al. (Ann Probab 23(1):236-267, 1995) for mean empirical measures. The class of processes we consider is determined by the martingale part of stochastic line integrals of 1-forms on a compact Riemannian manifold. For the pair of the current-valued process and mean empirical measures, we give an asymptotic evaluation of a nonlinear Laplace transform under a nondegeneracy assumption on th...
• Estimating the intensity of a random measure by histogram type estimators AI翻译
  作者：Baraud, Yannick; Birge, Lucien
  作者单位：Sorbonne Universite; Universite Paris Cite; Universite Cote d'Azur
  摘要：The purpose of this paper is to estimate the intensity of some random measure N on a set X by a piecewise constant function on a finite partition of X. Given a (possibly large) family M of candidate partitions, we build a piecewise constant estimator (histogram) on each of them and then use the data to select one estimator in the family. Choosing the square of a Hellinger-type distance as our loss function, we show that each estimator built on a given partition satisfies an analogue of the cla...
• Some local approximation properties of simple point processes AI翻译
  作者：Kallenberg, Olav
  作者单位：Auburn University System; Auburn University
  摘要：For simple point processes xi on a Borel space S, we prove some approximations involving conditional distributions, given that xi hits a small set B. Beginning with general versions of some classical limit theorems, going back to the pioneering work of Palm and Khinchin, we proceed to prove that, under suitable regularity conditions, the contributions to B and B-c are asymptotically conditionally independent. We further derive approximations in total variation of reduced Palm distributions and...
• Commutation relations and Markov chains AI翻译
  作者：Fulman, Jason
  作者单位：University of Southern California
  摘要：It is shown that the combinatorics of commutation relations is well suited for analyzing the convergence rate of certain Markov chains. Examples studied include random walk on irreducible representations, a local random walk on partitions whose stationary distribution is the Ewens distribution, and some birth-death chains.
• The loop-erased random walk and the uniform spanning tree on the four-dimensional discrete torus AI翻译
  作者：Schweinsberg, Jason
  作者单位：University of California System; University of California San Diego
  摘要：Let x and y be points chosen uniformly at random from Z(n)(4), the four-dimensional discrete torus with side length n. We show that the length of the loop-erased random walk from x to y is of order n(2)(log n)(1/6), resolving a conjecture of Benjamini and Kozma. We also show that the scaling limit of the uniform spanning tree on Z(n)(4) is the Brownian continuum random tree of Aldous. Our proofs use the techniques developed by Peres and Revelle, who studied the scaling limits of the uniform sp...
• Averaging principle for a class of stochastic reaction-diffusion equations AI翻译
  作者：Cerrai, Sandra; Freidlin, Mark
  作者单位：University of Florence; University System of Maryland; University of Maryland College Park
  摘要：We consider the averaging principle for stochastic reaction-diffusion equations. Under some assumptions providing existence of a unique invariant measure of the fast motion with the frozen slow component, we calculate limiting slow motion. The study of solvability of Kolmogorov equations in Hilbert spaces and the analysis of regularity properties of solutions, allow to generalize the classical approach to finite-dimensional problems of this type in the case of SPDE's.