-
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...
-
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.
-
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.
-
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).
