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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
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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...
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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.
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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...
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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...
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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...
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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.
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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...
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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.
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作者：Doumerc, Yan; Moriarty, John
作者单位：University of Manchester
摘要：We obtain a formula for the distribution of the first exit time of Brownian motion from the alcove of an affine Weyl group. In most cases the formula is expressed compactly, in terms of Pfaffians. Expected exit times are derived in the type (A) over tilde case. The results extend to other Markov processes. We also give formulas for the real eigenfunctions of the Dirichlet and Neumann Laplacians on alcoves, observing that the 'Hot Spots' conjecture of J. Rauch is true for alcoves.
