-
作者：Kargin, Vladislav
摘要：This paper derives sufficient conditions for superconvergence of sums of bounded free random variables and provides an estimate for the rate of superconvergence.
-
作者：Garet, Olivier; Marchand, Regine
作者单位：Universite de Orleans; Universite de Lorraine
摘要：The chemical distance D(x, y) is the length of the shortest open path between two points x and y in an infinite Bernoulli percolation cluster. In this work, we study the asymptotic behavior of this random metric, and we prove that, for an appropriate norm mu depending on the dimension and the percolation parameter, the probability of the event {0 <-> x, D(0, x)/mu(x) is not an element of (1 - epsilon, 1 + epsilon} exponentially decreases when vertical bar vertical bar x vertical bar vertical b...
-
作者：Chen, Xia
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：We study the upper tail behaviors of the local times of the additive stable processes. Let X-1 (t),..., X-p(t) be independent, d-dimensional symmetric stable processes with stable index 0 < alpha <= 2 and consider the additive stable process (X) over bar (t(1),..., t(p)) = X-1 (t(1)) + ... + X-p (t(p)). Under the condition d < alpha p, we obtain a precise form of the large deviation principle for the local time n(x)([0, t](p)) = integral(t)(o) ... integral(t)(o) delta(x)(X-1(s(1)) + ... + X-p ...
-
作者：Junge, Marius; Parcet, Javier; Xu, Quanhua
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; Autonomous University of Madrid; Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Instituto de Ciencias Matematicas (ICMAT); Universite Marie et Louis Pasteur
摘要：Let A denote the reduced amalgamated free product of a family A(1), A(2),..., A(n) of von Neumann algebras over a von Neumann subalgebra B with respect to normal faithful conditional expectations E-k: A(k) -> B. We investigate the norm in L-p (A) of homogeneous polynomials of a given degree d. We first generalize Voiculescu's inequality to arbitrary degree d >= 1 and indices 1 <= p <= infinity. This can be regarded as a free analogue of the classical Rosenthal inequality. Our second result is ...
-
作者：Watanabe, Toshiro
作者单位：University of Aizu
摘要：A necessary and sufficient condition for the almost sure existence of an absolutely continuous (with respect to the branching measure) exact Hausdorff measure on the boundary of a Galton-Watson tree is obtained. In the case where the absolutely continuous exact Hausdorff measure does not exist almost surely, a criterion which classifies gauge functions phi according to whether pi-Hausdorff measure of the boundary minus a certain exceptional set is zero or infinity is given. Important examples ...
-
作者：Kahn, Jeff; Weininger, Nicholas
摘要：A fractional fuzzy Potts measure is a probability distribution on spin configurations of a finite graph G obtained in two steps: first a subgraph of G is chosen according to a random cluster measure phi(p,q), and then a spin ( 1) is chosen independently for each component of the subgraph and assigned to all vertices of that component. We show that whenever q : 1, such a measure is positively associated, meaning that any two increasing events are positively correlated. This generalizes earlier ...
-
作者：Pinsky, Ross G.
作者单位：Technion Israel Institute of Technology
摘要：Let the random variable Z(n,k) denote the number of increasing subsequences of length k in a random permutation from S-n, the symmetric group of permutations of { 1,..., n }. In a recent paper [Random Structures Algorithms 29 (2006) 277-295] we showed that the weak law of large numbers holds for Z(n,kn,) if k(n) = o(n(2/5)); that is, lim(n ->infinity) Z (n,kn)/EZ(n,kn) = 1 in probability. The method of proof employed there used the second moment method and demonstrated that this method cannot ...
-
作者：Hult, Henrik; Lindskog, Filip
作者单位：Brown University; Royal Institute of Technology
摘要：We study the extremal behavior of a stochastic integral driven by a multivariate Levy process that is regularly varying with index alpha > 0. For predictable integrands with a finite (alpha + delta)-moment, for some delta > 0, we show that the extremal behavior of the stochastic integral is due to one big jump of the driving Levy process and we determine its limit measure associated with regular variation on the space of cadlag functions.
-
作者：Dembo, Amir; Peres, Yuval; Rosen, Jay
作者单位：Stanford University; Stanford University; City University of New York (CUNY) System; College of Staten Island (CUNY); University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：We show that the largest disccovered by a simple random walk (SRW) on Z(2) after n steps has radius n(1/4+o(1)), thus resolving an open problem of Revesz [Random Walk in Random and Non-Random Environments (1990) World Scientific, Teaneck, NJ]. For any fixed , the largest disc completely covered at least times by the SRW also has radius n(1/4+o(l)). However, the largest disc completely covered by each of E independent simple random walks on Z(2) after n steps is only of radius n (1/(2+2 root)+o...
-
作者：Russo, Francesco; Trutnau, Gerald
作者单位：Universite Paris 13; University of Bielefeld
摘要：A new class of random partial differential equations of parabolic type is considered, where the stochastic term consists of an irregular noisy drift, not necessarily Gaussian, for which a suitable interpretation is provided. After freezing a realization of the drift (stochastic process), we study existence and uniqueness (in some appropriate sense) of the associated parabolic equation and a probabilistic interpretation is investigated.
