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作者：Benjamini, Itai; Nachmias, Asaf; Peres, Yuval
作者单位：Weizmann Institute of Science; Microsoft
摘要：We show that the critical probability for percolation on a d-regular non-amenable graph of large girth is close to the critical probability for percolation on an infinite d-regular tree. We also prove a finite analogue of this statement, valid for expander graphs, without any girth assumption.
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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...
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作者：Bassetti, Federico; Ladelli, Lucia; Matthes, Daniel
作者单位：Polytechnic University of Milan; University of Pavia; Technische Universitat Wien
摘要：We introduce a class of kinetic-type equations on the real line, which constitute extensions of the classical Kac caricature. The collisional gain operators are defined by smoothing transformations with rather general properties. By establishing a connection to the central limit problem, we are able to prove long-time convergence of the equation's solutions toward a limit distribution. For example, we prove that if the initial condition belongs to the domain of normal attraction of a certain s...
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作者：Dupont, Christophe
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Let f be an holomorphic endomorphism of P-k and mu be its measure of maximal entropy. We prove an almost sure invariance principle for the systems (P-k, f, mu). Our class U of observables includes the Holder functions and unbounded ones which present analytic singularities. The proof is based on a geometric construction of a Bernoulli coding map omega : (Sigma, s, nu) -> (P-k, f, mu). We obtain the invariance principle for an observable psi on (P-k, f, mu) by applying Philipp-Stout's theorem f...
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作者：Chapuy, Guillaume
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
摘要：A unicellular map is a map which has only one face. We give a bijection between a dominant subset of rooted unicellular maps of given genus and a set of rooted plane trees with distinguished vertices. The bijection applies as well to the case of labelled unicellular maps, which are related to all rooted maps by Marcus and Schaeffer's bijection. This gives an immediate derivation of the asymptotic number of unicellular maps of given genus, and a simple bijective proof of a formula of Lehman and...
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作者：Ignatiouk-Robert, Irina
作者单位：CY Cergy Paris Universite
摘要：The complete representation of the Martin compactification for reflected random walks on a half-space Z(d) x N is obtained. It is shown that the full Martin compactification is in general not homeomorphic to the radial compactification obtained by Ney and Spitzer for the homogeneous random walks in Zd : convergence of a sequence of points z(n) is an element of Z(d-1) x N to a point of on the Martin boundary does not imply convergence of the sequence z(n)/vertical bar z(n)vertical bar on the un...
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作者：van der Hofstad, Remco; Holmes, Mark
作者单位：Eindhoven University of Technology; University of Auckland
摘要：We prove that the drift theta(d, beta) for excited random walk in dimension d is monotone in the excitement parameter beta is an element of [0, 1], when d is sufficiently large. We give an explicit criterion for monotonicity involving random walk Green's functions, and use rigorous numerical upper bounds provided by Hara (Private communication, 2007) to verify the criterion for d >= 9.
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作者：Ding, Jian; Lubetzky, Eyal; Peres, Yuval
作者单位：Microsoft; University of California System; University of California Berkeley
摘要：The cutoff phenomenon describes a case where a Markov chain exhibits a sharp transition in its convergence to stationarity. Diaconis [Proc Natl Acad Sci USA 93(4): 1659-1664, 1996] surveyed this phenomenon, and asked how one could recognize its occurrence in families of finite ergodic Markov chains. Peres [American Institute of Mathematics (AIM) Research Workshop, Palo Alto. http://www.aimath.org/WWN/mixingtimes, 2004] noted that a necessary condition for cutoff in a family of reversible chain...
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作者：Krylov, N. V.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We prove Ito's formula for the L (p)-norm of a stochastic W(p)1-valued processes appearing in the theory of SPDEs in divergence form.
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作者：Birkner, Matthias; Greven, Andreas; den Hollander, Frank
作者单位：University of Munich; University of Erlangen Nuremberg; Leiden University - Excl LUMC; Leiden University
摘要：When we cut an i.i.d. sequence of letters into words according to an independent renewal process, we obtain an i.i.d. sequence of words. In the annealed large deviation principle (LDP) for the empirical process of words, the rate function is the specific relative entropy of the observed law of words w.r.t. the reference law of words. In the present paper we consider the quenched LDP, i.e., we condition on a typical letter sequence. We focus on the case where the renewal process has an algebrai...
