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作者：Barlow, Martin T.; Cerny, Jiri
作者单位：University of British Columbia; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider a random walk among unbounded random conductances whose distribution has infinite expectation and polynomial tail. We prove that the scaling limit of this process is a Fractional-Kinetics process-that is the time change of a d-dimensional Brownian motion by the inverse of an independent alpha-stable subordinator. We further show that the same process appears in the scaling limit of the non-symmetric Bouchaud's trap model.
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作者：Morris, Robert
作者单位：University of Cambridge
摘要：We study zero-temperature Glauber dynamics on Z(d), which is a dynamic version of the Ising model of ferromagnetism. Spins are initially chosen according to a Bernoulli distribution with density p, and then the states are continuously (and randomly) updated according to the majority rule. This corresponds to the sudden quenching of a ferromagnetic system at high temperature with an external field, to one at zero temperature with no external field. Define p(c) (Z(d)) to be the infimum over p su...
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作者：Mirek, Mariusz
作者单位：University of Wroclaw
摘要：We consider the Markov chain {X-n(x)}(n=0)(infinity) = 0 on R-d defined by the stochastic recursion X-n(x) = psi(theta n) (X-n-1(x)), starting at x is an element of R-d, where theta(1), theta(2), ... are i.i.d. random variables taking their values in a metric space (Theta, r), and psi(theta n) : R-d -> R-d are Lipschitz maps. Assume that theMarkov chain has a unique stationary measure.. Under appropriate assumptions on psi(theta n) , we will show that the measure. has a heavy tail with the exp...
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作者：Banica, Teodor; Curran, Stephen; Speicher, Roland
作者单位：CY Cergy Paris Universite; University of California System; University of California Berkeley; Queens University - Canada
摘要：We consider several orthogonal quantum groups satisfying the easiness assumption axiomatized in our previous paper. For each of them we discuss the computation of the asymptotic law of Tr(u (k) ) with respect to the Haar measure, u being the fundamental representation. For the classical groups O (n) , S (n) we recover in this way some well-known results of Diaconis and Shahshahani.
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作者：Chen, Xin; Li, Xue-Mei; Wu, Bo
作者单位：University of Warwick; University of Warwick
摘要：The aim of the paper is to study the pinned Wiener measure on the loop space over a simply connected compact Riemannian manifold together with a Hilbert space structure and the Ornstein-Uhlenbeck operator d*d. We give a concrete estimate for the weak Poincar, inequality, assuming positivity of the Ricci curvature of the underlying manifold. The order of the rate function is s (-alpha) for any alpha > 0.
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作者：Nandori, Peter
作者单位：Budapest University of Technology & Economics
摘要：In the classical paper of Dvoretzky and ErdAs (Proceedings of the 2nd Berkeley Symposium on Mathematical Statistics and Probability, pp 353-367, 1951), asymptotics for the expected value and the variance of the number of distinct sites visited by a Simple Symmetric Random Walk were calculated. Here, these results are generalized for Random Walks with Internal States. Moreover, both weak and strong laws of large numbers are proved. As a tool for these results, the error term of the local limit ...
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作者：Rohde, Angelika
作者单位：University of Hamburg
摘要：Based on two independent samples X (1), . . . , X (m) and X (m+1), . . . , X (n) drawn from multivariate distributions with unknown Lebesgue densities p and q respectively, we propose an exact multiple test in order to identify simultaneously regions of significant deviations between p and q. The construction is built from randomized nearest-neighbor statistics. It does not require any preliminary information about the multivariate densities such as compact support, strict positivity or smooth...
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作者：Last, Guenter; Penrose, Mathew D.
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; University of Bath
摘要：We consider a Poisson process eta on an arbitrary measurable space with an arbitrary sigma-finite intensity measure. We establish an explicit Fock space representation of square integrable functions of eta. As a consequence we identify explicitly, in terms of iterated difference operators, the integrands in the Wiener-It chaos expansion. We apply these results to extend well-known variance inequalities for homogeneous Poisson processes on the line to the general Poisson case. The Poincar, ineq...
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作者：Bouleau, Nicolas; Denis, Laurent
作者单位：Universite Paris Saclay; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
摘要：We apply the Dirichlet form theory to stochastic differential equations with jumps as extension of Malliavin calculus reasoning. As in the continuous case, this weakens significantly the assumptions on the coefficients of the SDE. Thanks to the flexibility of the Dirichlet forms language, this approach brings also an important simplification which was neither available nor visible previously: an explicit formula giving the carr, du champ matrix, i.e., the Malliavin matrix. Following this formu...
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作者：Vershynin, Roman
作者单位：University of Michigan System; University of Michigan
摘要：We study the spectral norm of matrices W that can be factored as W = BA, where A is a random matrix with independent mean zero entries and B is a fixed matrix. Under the (4 + epsilon)th moment assumption on the entries of A, we show that the spectral norm of such an m x n matrix W is bounded by root m + root n, which is sharp. In other words, in regard to the spectral norm, products of random and deterministic matrices behave similarly to random matrices with independent entries. This result a...
