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作者：Adams, Terrence M.; Nobel, Andrew B.
作者单位：United States Department of Defense; University of North Carolina; University of North Carolina Chapel Hill
摘要：We show that if X is a complete separable metric space and C is a countable family of Borel subsets of X with finite VC dimension, then, for every stationary ergodic process with values in X, the relative frequencies of sets C is an element of C converge uniformly to their limiting probabilities Beyond ergodicity. no assumptions are imposed on the sampling process. and no regularity conditions are imposed on the elements of C The result extends existing work of Vapnik and Chervonenkis among ot...
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作者：Barlow, M. T.; Deuschel, J-D.
作者单位：University of British Columbia; Technical University of Berlin
摘要：We study a continuous time random walk X in an environment of i.i.d. random conductances mu(e) is an element of [1, infinity). We obtain heat kernel bounds and prove a quenched invariance principle for X. This holds even when E mu(e) = infinity.
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作者：Panchenko, Dmitry
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：We consider a symmetric positive definite weakly exchangeable infinite random matrix and show that, under the technical condition that its elements take a finite number of values, the Ghirlanda-Guerra identities imply ultrametricity.
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作者：Fribergh, Alexander
作者单位：New York University
摘要：We study the speed of a biased random walk on a percolation cluster on Z(d) in function of the percolation parameter p. We obtain a first order expansion of the speed at p = 1 which proves that percolating slows down the random walk at least in the case where the drift is along a component of the lattice.
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作者：Klenke, Achim; Oeler, Mario
作者单位：Johannes Gutenberg University of Mainz
摘要：Dawson and Perkins [Ann. Probab. 26 (1988) 1088-1138] constructed a stochastic model of an interacting two-type population indexed by a countable site space which locally undergoes a mutually catalytic branching mechanism. In Klenke and Mytnik [Preprint (2008), arXiv:0901.0623], it is shown that as the branching rate approaches infinity, the process converges to a process that is called the infinite rate mutually catalytic branching process (IMUB). It is most conveniently characterized as the ...
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作者：Roy, Parthanil
作者单位：Michigan State University
摘要：We consider a point process sequence induced by a stationary symmetric alpha-stable (0 < alpha < 2) discrete parameter random field. It is easy to prove, following the arguments in the one-dimensional case in [Stochastic Process. Appl. 114 (2004) 191-210], that if the random field is generated by a dissipative group action then the point process sequence converges weakly to a cluster Poisson process. For the conservative case, no general result is known even in the one-dimensional case. We loo...
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作者：Katalin Marton
作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Hungarian Academy of Sciences
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作者：Peterson, Jonathon; Seppaelaeinen, Timo
作者单位：Cornell University; University of Wisconsin System; University of Wisconsin Madison
摘要：We study the current of particles that move independently in a common static random environment on the one-dimensional integer lattice. A two-level fluctuation picture appears. On the central limit scale the quenched mean of the current process converges to a Brownian motion. On a smaller scale the current process centered at its quenched mean converges to a mixture of Gaussian processes. These Gaussian processes are similar to those arising from classical random walks, but the environment mak...
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作者：Gotze, Friedrich; Tikhomirov, Alexander
作者单位：University of Bielefeld; Saint Petersburg State University
摘要：We consider the joint distribution of real and imaginary parts of eigen-values of random matrices with Independent entries with mean zero and unit variance We prove the convergence of this distribution to the uniform distribution on the unit disc without assumptions on the existence of a density for the distribution of entries We assume that the entries have a finite moment of order larger than two and consider the case of sparse matrices The results are based on previous work of Bai, Rudelson...
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作者：Doney, R. A.; Savov, M. S.
作者单位：University of Manchester; Sorbonne Universite
摘要：If X is a stable process of index alpha is an element of (0, 2) whose Levy measure has density cx(-alpha-1) on (0, infinity), and S(1) = sup(0<= 1) X(t), it is known that P(S(1) > x) similar to A alpha-1 x-alpha as x -> infinity and P(S(1) <= x) similar to B alpha(-1) rho(-1) x(alpha rho) as x down arrow 0. [Here rho = (X(1) > 0) and A and B are known constants.] It is also known that S(1) has a continuous density, m say. The main point of this note is to show that m(x) similar to Ax(-(alpha+1...
