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作者：Rider, B.; Silverstein, Jack W.
作者单位：University of Colorado System; University of Colorado Boulder; North Carolina State University
摘要：Consider an ensemble of N x N non-Hermitian matrices in which all entries are independent identically distributed complex random variables of mean zero and absolute mean-square one. If the entry distributions also possess bounded densities and finite (4 + epsilon) moments, then Z. D. Bai [Ann. Probab. 25 (1997) 494-529] has shown the ensemble to satisfy the circular law: after scaling by a factor of 1/root N and letting N -> infinity, the empirical measure Of the eigenvalues converges weakly t...
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作者：Chassaing, Philippe; Durhuus, Bergfinnur
作者单位：Universite de Lorraine; University of Copenhagen; University of Copenhagen
摘要：Exploiting a bijective correspondence between planar quadrangulations and well-labeled trees, we define an ensemble of infinite surfaces as a limit of uniformly distributed ensembles of quadrangulations of fixed finite volume. The limit random surface can be described in terms of a birth and death process and a sequence of multitype Galton-Watson trees. As a consequence, we find that the expected volume of the ball of radius r around a marked point in the limit random surface is Theta(r(4)).
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作者：Dembo, A; Peres, Y; Rosen, J; Zeitouni, O
作者单位：Stanford University; Stanford University; City University of New York (CUNY) System; College of Staten Island (CUNY); University of California System; University of California Berkeley; University of California System; University of California Berkeley; Technion Israel Institute of Technology; Technion Israel Institute of Technology; University of Minnesota System; University of Minnesota Twin Cities
摘要：Let T-n(x) denote the time of first visit of a point x on the lattice torus Z(n)(2) = Z(2)/nZ(2) by the simple random walk. The size of the set of alpha, n-late points L-n(alpha) = {x is an element of Z(n)(2): T-n(x) >= alpha(4)/(pi)(n log n)(2)} is approximately n(2(1-alpha)), for alpha is an element of (0, 1) [L-n(alpha) is empty if alpha > 1 and n is large enough]. These sets have interesting clustering and fractal properties: we show that for beta is an element of (0, 1), a disc of radius ...
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作者：Seidenfeld, T; Schervish, MJ; Kadane, JB
作者单位：Carnegie Mellon University; Carnegie Mellon University
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作者：Bahadoran, C.; Guiol, H.; Ravishankar, K.; Saada, E.
作者单位：Universite Clermont Auvergne (UCA); State University of New York (SUNY) System; University at Albany, SUNY; SUNY New Paltz; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider attractive irreducible conservative particle systems on Z, without necessarily nearest-neighbor jumps or explicit invariant measures. We prove that for such systems, the hydrodynamic limit under Enter time scaling exists and is given by the entropy solution to some scalar conservation law with Lipschitz-continuous flux. Our approach is a generalization of Bahadoran et al. [Stochastic Process. Appl. 99 (2002) 1-30], from which we relax the assumption that the process has explicit in...
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作者：Mathieu, Pierre
作者单位：Aix-Marseille Universite
摘要：We extend the Carne-Varopoulos upper bound on the probability transitions of a Markov chain to a certain class of nonreversible processes by introducing the definition of a centering measure. In the case of random walks on a group, we study the connections between different notions of centering.
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作者：Timar, Adam
作者单位：Indiana University System; Indiana University Bloomington
摘要：We show that for a transitive unimodular graph, the number of ends is the same for every tree of the free minimal spanning forest. This answers a question of Lyons, Peres and Schramm.
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作者：Berestycki, Nathanael
作者单位：University of British Columbia; Universite PSL; Ecole Normale Superieure (ENS)
摘要：Turn the set of permutations of n objects into a graph G, by connecting two permutations that differ by one transposition, and let at be the simple random walk on this graph. In a previous paper, Berestycki and Durrett [In Discrete Random Walks (2005) 17-26] showed that the limiting behavior of the distance from the identity at time cn/2 has a phase transition at c = 1. Here we investigate some consequences of this result for the geometry of G, Our first result can be interpreted as a breakdow...
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作者：Yukich, JE; Zhang, Y
作者单位：Lehigh University; University of Colorado System; University of Colorado at Colorado Springs
摘要：Let 0 < a < b < infinity be fixed scalars. Assign independently to each edge in the lattice Z(2) the value a with probability p or the value b with probability 1 - p. For all u, v is an element of Z(2), let T(u, v) denote the first passage time between u and v. We show that there are points x is an element of R-2 such that the time constant in the direction of x, namely, lim(n ->infinity) n(-1) E-p[T(0, nx)], is not a three times differentiable function of p.
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作者：Hammond, Alan
作者单位：University of California System; University of California Berkeley
摘要：Assign to each site of the integer lattice Z(d) a real score, sampled according to the same distribution F, independently of the choices made at all other sites. A lattice animal is a finite connected set of sites, with its weight being the sum of the scores at its sites. Let N-n be the maximal weight of those lattice animals of size if that contain the origin. Denote by N the almost sure finite constant limit of n(-1) N-n which exists under a mild condition on the positive tail of F. We study...
