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作者：Wang, FY
作者单位：Beijing Normal University; University of Bielefeld
摘要：By using the maximum principle and analysis of heat semigroups, Harnack inequalities are studied for log-Sobolev functions. From this, some lower bound estimates of the log-Sobolev constant are presented by using the spectral gap inequality and the coupling method. The resulting inequalities either recover or improve the corresponding ones proved by Chung and Yau. Especially, Harnack inequalities and estimates of log-Sobolev constants can be dimension-free.
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作者：Pitman, J
作者单位：University of California System; University of California Berkeley
摘要：For each finite measure Lambda on [0, 1], a coalescent Markov process, with state space the compact set of all partitions of the set N of positive integers, is constructed so the restriction of the partition to each finite subset of N is a Markov chain with the following transition rates: when the partition has b blocks, each K-tuple of blocks is merging to form a single block at rate integral(0)(1) x(k-2) (1 - x)(b-k)Lambda(dx). Call this process a Lambda-coalescent. Discrete measure-valued p...
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作者：Sznitman, AS; Zerner, MPW
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We derive a law of large numbers for a class of multidimensional random walks in random environment satisfying a condition which first appeared in the work of Kalikow. The approach is based on the existence of a renewal structure under an assumption of transience in the direction l. This extends, to a multidimensional context, previous work of Kesten. Our results also enable proving the convergence of the law of the environment viewed from the particle toward a limiting distribution.
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作者：Delmas, JF
作者单位：Institut Polytechnique de Paris; Ecole des Ponts ParisTech
摘要：We first consider a super Brownian motion X with a general branching mechanism. Using the Brownian snake representation with subordination, we get the Hausdorff dimension of supp X-t, the topological support of X-t and, more generally, the Hausdorff dimension of U-t is an element of B supp X-t. We also provide estimations on the hitting probability of small balls for those random measures. We then deduce that the support is totally disconnected in high dimension. Eventually, considering a supe...
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作者：Latala, R; Oleszkiewicz, K
作者单位：University of Warsaw
摘要：We prove that the inequality Psi(-1)(mu(tA)) greater than or equal to t Psi(-1)(mu(A)) holds for any centered Gaussian measure Cc on a separable Banach space F, any convex, closed, symmetric set A subset of F and t greater than or equal to 1, where Psi(x) = gamma(1)(-x, x) = (2 pi)(-1/2) integral(-x)(x) exp(-y(2)/2) dy. As an application, the best constants in comparison of moments of Gaussian vectors are calculated.
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作者：Fannjiang, A; Komorowski, T
作者单位：University of California System; University of California Davis; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We prove an almost sure invariance principle for diffusion driven by velocities with unbounded stationary vector potentials. The result generalizes to multiple particles motion, driven by a common velocity field and independent molecular Brownian motions.
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作者：Benjamini, I; Lyons, R; Peres, Y; Schramm, O
作者单位：Weizmann Institute of Science; Hebrew University of Jerusalem; University of California System; University of California Berkeley; Indiana University System; Indiana University Bloomington
摘要：We show that independent percolation on any Cayley graph of a nonamenable group has no infinite components at the critical parameter. This result was obtained by the present authors earlier as a corollary of a general study of group-invariant percolation. The goal here is to present a simpler self-contained proof that easily extends to quasi-transitive graphs with a unimodular automorphism group. The key tool is a mass-transport method, which is a technique of averaging in nonamenable settings.
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作者：Hsing, T
作者单位：National University of Singapore; Texas A&M University System; Texas A&M University College Station
摘要：This paper investigates the asymptotic distribution of the partial sum S-N = Sigma(n=1)(N)[K(X-n) - EK(X-n)], as N --> infinity, where {X-n} is a moving average stable process and K is a bounded and measurable function. The results show that SN follows a central or non-central limit theorem depending on the rate at which the moving average coefficients tend to 0.
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作者：Lyons, R; Schramm, O
作者单位：Indiana University System; Indiana University Bloomington; Weizmann Institute of Science
摘要：We show that when percolation produces infinitely many infinite dusters on a Cayley graph, one cannot distinguish the clusters from each other by any invariantly defined property. This implies that uniqueness of the infinite cluster is equivalent to nondecay of connectivity (a.k.a. long-range order). We then derive applications concerning uniqueness in Kazhdan groups and in wreath products and inequalities for p(u).
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作者：Bai, ZD; Silverstein, JW
作者单位：National University of Singapore; North Carolina State University
摘要：Let B-n = (1/N)T-n(1/2) X-n (XnTn1/2)-T-* where X-n is n x N with i.i.d. complex standardized entries having finite fourth moment, and T-n(1/2) is a Hermitian square root of the nonnegative definite Hermitian matrix T-n. It was shown in an earlier paper by the authors that, under certain conditions on the eigenvalues of T-n, with probability 1 no eigenvalues lie in any interval which is outside the support of the limiting empirical distribution (known to exist) for all large rt. For these n th...
