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作者：Merlevede, Florence; Peligrad, Magda
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); University System of Ohio; University of Cincinnati
摘要：The aim of this paper is to propose new Rosenthal-type inequalities for moments of order higher than 2 of the maximum of partial sums of stationary sequences including martingales and their generalizations. As in the recent results by Peligrad et al. [Proc. Amer. Math. Soc. 135 (2007) 541-550] and Rio [J. Theoret. Probab. 22 (2009) 146-163], the estimates of the moments are expressed in terms of the norms of projections of partial sums. The proofs of the results are essentially based on a new ...
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作者：Mossel, Elchanan; Sly, Allan
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：We establish tight results for rapid mixing of Gibbs samplers for the Ferromagnetic Ising model on general graphs. We show that if (d - 1) tanh beta < 1, then there exists a constant C such that the discrete time mixing time of Gibbs samplers for the ferromagnetic Ising model on any graph of n vertices and maximal degree d, where all interactions are bounded by beta, and arbitrary external fields are bounded by Cn log n. Moreover, the spectral gap is uniformly bounded away from 0 for all such ...
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作者：Oliveira, Roberto Imbuzeiro
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：The main results in this paper are about the full coalescence time C of a system of coalescing random walks over a finite graph G. Letting m(G) denote the mean meeting time of two such walkers, we give sufficient conditions under which E[C] approximate to 2m(G) and C/m(G) has approximately the same law as in the mean field setting of a large complete graph. One of our theorems is that mean field behavior occurs over all vertex-transitive graphs whose mixing times are much smaller than m(G); th...
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作者：Le Gall, Jean-Francois
作者单位：Universite Paris Saclay
摘要：We consider a random planar map M-n which is uniformly distributed over the class of all rooted q-angulations with n faces. We let m(n) be the vertex set of M-n, which is equipped with the graph distance d(gr). Both when q >= 4 is an even integer and when q = 3, there exists a positive constant c(q) such that the rescaled metric spaces (m(n), c(q)n(-1/4)d(gr)) converge in distribution in the Gromov-Hausdorff sense, toward a universal limit called the Brownian map. The particular case of triang...
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作者：Bovier, Anton; Gayrard, Veronique
作者单位：University of Bonn; Aix-Marseille Universite
摘要：We derive a general criterion for the convergence of clock processes in random dynamics in random environments that is applicable in cases when correlations are not negligible, extending recent results by Gayrard [(2010), (2011), forthcoming], based on general criterion for convergence of sums of dependent random variables due to Durrett and Resnick [Ann. Probab. 6 (1978) 829-846]. We demonstrate the power of this criterion by applying it to the case of random hopping time dynamics of the p-sp...
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作者：Auffinger, Antonio; Ben Arous, Gerard
作者单位：University of Chicago; New York University
摘要：We analyze the landscape of general smooth Gaussian functions on the sphere in dimension N, when N is large. We give an explicit formula for the asymptotic complexity of the mean number of critical points of finite and diverging index at any level of energy and for the mean Euler characteristic of level sets. We then find two possible scenarios for the bottom landscape, one that has a layered structure of critical values and a strong correlation between indexes and critical values and another ...
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作者：Ledrappier, Francois
作者单位：University of Notre Dame; Sorbonne Universite
摘要：We consider nondegenerate, finitely supported random walks on a finitely generated Gromov hyperbolic group. We show that the entropy and the escape rate are Lipschitz functions of the probability if the support remains constant.
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作者：Gloter, Arnaud; Martinez, Miguel
作者单位：Universite Paris Saclay; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：In this paper, we consider two skew Brownian motions, driven by the same Brownian motion, with different starting points and different skewness coefficients. We show that we can describe the evolution of the distance between the two processes with a stochastic differential equation. This S.D.E. possesses a jump component driven by the excursion process of one of the two skew Brownian motions. Using this representation, we show that the local time of two skew Brownian motions at their first hit...
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作者：Drapeau, Samuel; Heyne, Gregor; Kupper, Michael
作者单位：Humboldt University of Berlin
摘要：We study the nonlinear operator of mapping the terminal value xi to the corresponding minimal supersolution of a backward stochastic differential equation with the generator being monotone in y, convex in z, jointly lower semicontinuous and bounded below by an affine function of the control variable z. We show existence, uniqueness, monotone convergence, Fatou's lemma and lower semicontinuity of this operator. We provide a comparison principle for minimal supersolutions of BSDEs.
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作者：Lee, James R.; Peres, Yuval
作者单位：University of Washington; University of Washington Seattle; Microsoft
摘要：We prove diffusive lower bounds on the rate of escape of the random walk on infinite transitive graphs. Similar estimates hold for finite graphs, up to the relaxation time of the walk. Our approach uses nonconstant equivariant harmonic mappings taking values in a Hilbert space. For the special case of discrete, amenable groups, we present a more explicit proof of the Mok-Korevaar-Schoen theorem on the existence of such harmonic maps by constructing them from the heat flow on a Folner set.
