-
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...
-
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...
-
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...
-
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.
-
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...
-
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.
-
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...
-
作者：Mossel, Elchanan; Sly, Allan
作者单位：University of California System; University of California Berkeley
摘要：Gibbs sampling also known as Glauber dynamics is a popular technique for sampling high dimensional distributions defined on graphs. Of special interest is the behavior of Gibbs sampling on the Erdos-Renyi random graph G(n, d/n), where each edge is chosen independently with probability d/n and d is fixed. While the average degree in G(n, d/n) is d(1-o(1)), it contains many nodes of degree of order (log n)/(log log n). The existence of nodes of almost logarithmic degrees implies that for many na...
-
作者：Kifer, Yuri
作者单位：Hebrew University of Jerusalem
摘要：The polynomial ergodic theorem ( PET) which appeared in Bergelson (Ergod. Th. Dynam. Sys. 7, 337-349, 1987) and attracted substantial attention in ergodic theory studies the limits of expressions having the form 1/N Sigma(N)(n=1) T-q1(n) f(1) ... T-ql(n) f(l) where T is a weakly mixing measure preserving transformation, f(i)'s are bounded measurable functions and q(i)'s are polynomials taking on integer values on the integers. Motivated partially by this result we obtain a central limit theore...
-
作者：Mariani, Mauro
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：Large deviations principles for a family of scalar 1 + 1 dimensional conservative stochastic PDEs (viscous conservation laws) are investigated, in the limit of jointly vanishing noise and viscosity. A first large deviations principle is obtained in a space of Young measures. The associated rate functional vanishes on a wide set, the so-called set of measure-valued solutions to the limiting conservation law. A second order large deviations principle is therefore investigated, however, this can ...
