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作者：Restrepo, Ricardo; Shin, Jinwoo; Tetali, Prasad; Vigoda, Eric; Yang, Linji
作者单位：Universidad de Antioquia; University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology
摘要：The hard-core model has received much attention in the past couple of decades as a lattice gas model with hard constraints in statistical physics, a multicast model of calls in communication networks, and as a weighted independent set problem in combinatorics, probability and theoretical computer science. In this model, each independent set I in a graph G is weighted proportionally to lambda(|I|), for a positive real parameter lambda. For large lambda, computing the partition function (namely,...
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作者：Shcherbina, T.
作者单位：National Academy of Sciences Ukraine; B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine
摘要：We consider asymptotic behavior of the correlation functions of the characteristic polynomials of the hermitian sample covariance matrices , where A (m,n) is a m x n complex random matrix with independent and identically distributed entries and . We show that for the correlation function of any even order the asymptotic behavior in the bulk and at the edge of the spectrum coincides with those for the Gaussian Unitary Ensemble up to a factor, depending only on the fourth moment of the common pr...
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作者：Xiao, Yimin; Zheng, Xinghua
作者单位：Michigan State University; Hong Kong University of Science & Technology
摘要：Let be a continuous time random walk in an environment of i.i.d. random conductances , where E (d) is the set of nonoriented nearest neighbor bonds on the Euclidean lattice and d a parts per thousand yen 3. Let be the range of X. It is proved that, for almost every realization of the environment, dim(H) R = dim(P) R = 2 almost surely, where dim(H) and dim(P) denote, respectively, the discrete Hausdorff and packing dimension. Furthermore, given any set , a criterion for A to be hit by X (t) for...
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作者：Arguin, Louis-Pierre; Chatterjee, Sourav
作者单位：Universite de Montreal; New York University
摘要：Random overlap structures (ROSt's) are random elements on the space of probability measures on the unit ball of a Hilbert space, where two measures are identified if they differ by an isometry. In spin glasses, they arise as natural limits of Gibbs measures under the appropriate algebra of functions. We prove that the so called 'cavity mapping' on the space of ROSt's is continuous, leading to a proof of the stochastic stability conjecture for the limiting Gibbs measures of a large class of spi...
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作者：Croydon, D. A.; Fribergh, A.; Kumagai, T.
作者单位：University of Warwick; New York University; Kyoto University
摘要：We consider the biased random walk on a critical Galton-Watson tree conditioned to survive, and confirm that this model with trapping belongs to the same universality class as certain one-dimensional trapping models with slowly-varying tails. Indeed, in each of these two settings, we establish closely-related functional limit theorems involving an extremal process and also demonstrate extremal aging occurs.
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作者：Gordina, Maria; Melcher, Tai
作者单位：University of Connecticut; University of Virginia
摘要：Let G denote an infinite-dimensional Heisenberg-like group, which is a class of infinite-dimensional step 2 stratified Lie groups. We consider holomorphic functions on G that are square integrable with respect to a heat kernel measure which is formally subelliptic, in the sense that all appropriate finite-dimensional projections are smooth measures. We prove a unitary equivalence between a subclass of these square integrable holomorphic functions and a certain completion of the universal envel...
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作者：Alsmeyer, Gerold; Meiners, Matthias
作者单位：University of Munster; Uppsala University
摘要：Given a sequence (C, T) = (C, T (1), T (2), . . .) of real-valued random variables with T (j) a parts per thousand yen 0 for all j a parts per thousand yen 1 and almost surely finite N = sup{j a parts per thousand yen 1 : T (j) > 0}, the smoothing transform associated with (C, T), defined on the set of probability distributions on the real line, maps an element to the law of , where X (1), X (2), . . . is a sequence of i.i.d. random variables independent of (C, T) and with distribution P. We s...
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作者：Chistyakov, G. P.; Goetze, F.
作者单位：University of Bielefeld; National Academy of Sciences Ukraine; B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine
摘要：We prove Edgeworth type expansions for distribution functions of sums of free random variables under minimal moment conditions. The proofs are based on the analytic definition of free convolution.
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作者：van den Berg, J.; Gandolfi, A.
作者单位：Centrum Wiskunde & Informatica (CWI); Vrije Universiteit Amsterdam; University of Florence
摘要：Recently, van den Berg and Jonasson gave the first substantial extension of the BK inequality for non-product measures: they proved that, for -out-of- measures, the probability that two increasing events occur disjointly is at most the product of the two individual probabilities. We show several other extensions and modifications of the BK inequality. In particular, we prove that the antiferromagnetic Ising Curie-Weiss model satisfies the BK inequality for all increasing events. We prove that ...
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作者：Rider, Brian; Sinclair, Christopher D.; Xu, Yuan
作者单位：University of Colorado System; University of Colorado Boulder; University of Oregon
摘要：We consider an ensemble of interacting charged particles on the line consisting of two species of particles with charge ratio 2:1 in the presence of an external field. With the total charge fixed and the system held at temperature corresponding to beta = 1, it is proved that the particles form a Pfaffian point process. When the external field is quadratic (the harmonic oscillator potential), we produce the explicit family of skew-orthogonal polynomials necessary to simplify the related matrix ...
