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作者：Sidoravicius, V; Sznitman, AS
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA); Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：In this work we principally study random walk on the supercritical infinite cluster for bond percolation on Z(d). We prove a quenched functional central limit theorem for the walk when dgreater than or equal to4. We also prove a similar result for random walk among i.i.d. random conductances along nearest neighbor edges of Z(d), when dgreater than or equal to1.
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作者：Johnson, O; Barron, A
作者单位：University of Cambridge; Yale University
摘要：We give conditions for an O(1/n) rate of convergence of Fisher information and relative entropy in the Central Limit Theorem. We use the theory of projections in L-2 spaces and Poincare inequalities, to provide a better understanding of the decrease in Fisher information implied by results of Barron and Brown. We show that if the standardized Fisher information ever becomes finite then it converges to zero.
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作者：Orsingher, E; Beghin, L
作者单位：Sapienza University Rome
摘要：We study the fundamental solutions to time-fractional telegraph equations of order 2alpha. We are able to obtain the Fourier transform of the solutions for any alpha and to give a representation of their inverse, in terms of stable densities. For the special case alpha=1/2, we can show that the fundamental solution is the distribution of a telegraph process with Brownian time. In a special case, this becomes the density of the iterated Brownian motion, which is therefore the fundamental soluti...
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作者：Lawler, GF; Werner, W
作者单位：Cornell University; Universite Paris Saclay
摘要：We define a natural conformally invariant measure on unrooted Brownian loops in the plane and study some of its properties. We relate this measure to a measure on loops rooted at a boundary point of a domain and show how this relation gives a way to chronologically add Brownian loops to simple curves in the plane.
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作者：Hiai, F; Petz, D; Ueda, Y
作者单位：Tohoku University; Budapest University of Technology & Economics; Kyushu University
摘要：By means of random matrix approximation procedure, we re-prove Biane and Voiculescu's free analog of Talagranda's transportation cost inequality for measures on R in a more general setup. Furthermore, we prove the free transportation cost inequality for measures on T as well by extending the method to special unitary random matrices.
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作者：Biskup, M; Blanchard, P; Chayes, L; Gandolfo, D; Krüger, T
作者单位：University of California System; University of California Los Angeles; University of Bielefeld; Universite de Toulon; Aix-Marseille Universite
摘要：We study a model of ''organized'' criticality, where a single avalanche propagates through an a priori static (i.e., organized) sandpile configuration. The latter is chosen according to an i.i.d. distribution from a Borel probability measure rho on [0,1]. The avalanche dynamics is driven by a standard toppling rule, however, we simplify the geometry by placing the problem on a directed, rooted tree. As our main result, we characterize which rho are critical in the sense that they do not admit ...
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作者：Gao, ZC; Wormald, NC
作者单位：University of Macau; University of Waterloo; University of Melbourne
摘要：We give a general result showing that the asymptotic behaviour of high moments determines the shape of distributions which are asymptotically normal. Both the factorial and non-factorial (non-central) moments are treated. This differs from the usual moment method in combinatorics, as the expected value may tend to infinity quite rapidly. Applications are given to submap counts in random planar triangulations, where we use a simple argument to asymptotically determine high moments for the numbe...
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作者：Chen, X; Li, WV
作者单位：University of Tennessee System; University of Tennessee Knoxville; University of Delaware
摘要：We study the large and moderate deviations for intersection local times generated by, respectively, independent Brownian local times and independent local times of symmetric random walks. Our result in the Brownian case generalizes the large deviation principle achieved in Mansmann (1991) for the L-2-norm of Brownian local times, and coincides with the large deviation obtained by Csorgo, Shi and Yor (1999) for self intersection local times of Brownian bridges. Our approach relies on a Feynman-...
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作者：Rider, B
作者单位：Duke University
摘要：Consider Ginibre's ensemble of N x N non-Hermitian random matrices in which all entries are independent complex Gaussians of mean zero and variance 1/N.As N up arrow infinity the normalized counting measure of the eigenvalues converges to the uniform measure on the unit disk in the complex plane. In this note we describe fluctuations about this Circular Law. First we obtain finite N formulas for the covariance of certain linear statistics of the eigenvalues. Asymptotics of these objects couple...
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作者：Kim, KH
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Stochastic partial differential equations of divergence form are considered in C-1 domains. Existence and uniqueness results are given in a Sobolev space with weights allowing the derivatives of the solutions to blow up near the boundary.
