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作者：Lacoin, Hubert
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：In this paper, we investigate the mixing time of the adjacent transposition shuffle for a deck of N cards. We prove that around time N-2 logN/(2 pi(2)), the total variation distance to equilibrium of the deck distribution drops abruptly from 1 to 0, and that the separation distance has a similar behavior but with a transition occurring at time (N-2 logN)/pi(2). This solves a conjecture formulated by David Wilson. We present also similar results for the exclusion process on a segment of length ...
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作者：Baudoin, F.; Nualart, E.; Ouyang, C.; Tindel, S.
作者单位：Purdue University System; Purdue University; Pompeu Fabra University; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Universite de Lorraine
摘要：This article investigates several properties related to densities of solutions (X-t)(t is an element of[0,1]) to differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/4. We first determine conditions for strict positivity of the density of X-t. Then we obtain some exponential bounds for this density when the diffusion coefficient satisfies an elliptic type condition. Finally, still in the elliptic case, we derive some bounds on the hitting probabilities of se...
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作者：Berger, Noam; Cohen, Moran; Rosenthal, Ron
作者单位：Hebrew University of Jerusalem; Technical University of Munich; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：In this work, we discuss certain ballistic random walks in random environments on Z(d), and prove the equivalence between the static and dynamic points of view in dimension d >= 4. Using this equivalence, we also prove a version of a local limit theorem which relates the local behavior of the quenched and annealed measures of the random walk by a prefactor.
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作者：Debussche, Arnaud; Hofmanova, Martina; Vovelle, Julien
作者单位：Ecole Normale Superieure de Rennes (ENS Rennes); Max Planck Society; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：In this paper, we study the Cauchy problem for a quasilinear degenerate parabolic stochastic partial differential equation driven by a cylindrical Wiener process. In particular, we adapt the notion of kinetic formulation and kinetic solution and develop a well-posedness theory that includes also an L-1-contraction property. In comparison to the previous works of the authors concerning stochastic hyperbolic conservation laws [J. Funct. Anal. 259 (2010) 1014-1042] and semilinear degenerate parab...
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作者：Jirak, Moritz
作者单位：Humboldt University of Berlin
摘要：Let {X-k}(k >= Z) be a stationary sequence. Given p is an element of (2, 3] moments and a mild weak dependence condition, we show a Berry-Esseen theorem with optimal rate n(p/2-1). For p >= 4, we also show a convergence rate of n(1/2) in L-q-norm, where q >= 1. Up to log n factors, we also obtain nonuniform rates for any p > 2. This leads to new optimal results for many linear and nonlinear processes from the time series literature, but also includes examples from dynamical system theory. The ...
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作者：Duminil-Copin, Hugo; Glazman, Alexander; Hammond, Alan; Manolescu, Ioan
作者单位：University of Geneva; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Scientific Centre of the Russian Academy of Sciences; University of Oxford
摘要：We prove two results on the delocalization of the endpoint of a uniform self-avoiding walk on Z(d) for d >= 2. We show that the probability that a walk of length n ends at a point x tends to 0 as n tends to infinity, uniformly in x. Also, when x is fixed, with parallel to x parallel to = 1, this probability decreases faster than n(-1/4+epsilon) for any epsilon > 0. This provides a bound on the probability that a self-avoiding walk is a polygon.
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作者：Tang, Shanjian; Wei, Wenning
作者单位：Fudan University
摘要：This paper is concerned with solution in Holder spaces of the Cauchy problem for linear and semi-linear backward stochastic partial differential equations (BSPDEs) of super-parabolic type. The pair of unknown variables are viewed as deterministic spatial functionals which take values in Banach spaces of random (vector) processes. We define suitable functional Holder spaces for them and give some inequalities among these Holder norms. The existence, uniqueness as well as the regularity of solut...
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作者：Hutchcroft, Tom
作者单位：University of British Columbia
摘要：We prove that every component of the wired uniform spanning forest (WUSF) is one-ended almost surely in every transient reversible random graph, removing the bounded degree hypothesis required by earlier results. We deduce that every component of the WUSF is one-ended almost surely in every supercritical Galton Watson tree, answering a question of Benjamini, Lyons, Peres and Schramm [Ann. Probab. 29 (2001) 1-65]. Our proof introduces and exploits a family of Markov chains under which the orien...
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作者：Goldschmidt, Christina; Haas, Benedicte
作者单位：University of Oxford; Universite PSL; Universite Paris-Dauphine
摘要：We study a Markovian model for the random fragmentation of an object. At each time, the state consists of a collection of blocks. Each block waits an exponential amount of time with parameter given by its size to some power a, independently of the other blocks. Every block then splits randomly into sub-blocks whose relative sizes are distributed according to the so-called dislocation measure. We focus here on the case where alpha < 0. In this case, small blocks split intensively, and so the wh...
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作者：Quas, Anthony; Soo, Terry
作者单位：University of Victoria; University of Kansas
摘要：Sinai proved that a nonatomic ergodic measure-preserving system has any Bernoulli shift of no greater entropy as a factor. Given a Bernoulli shift, we show that any other Bernoulli shift that is of strictly less entropy and is stochastically dominated by the original measure can be obtained as a monotone factor; that is, the factor map has the property that for each point in the domain, its image under the factor map is coordinatewise smaller than or equal to the original point.
