-
作者：Kaj, Ingemar; Leskela, Lasse; Norros, Ilkka; Schmidt, Volker
作者单位：Uppsala University; Aalto University; Ulm University
摘要：This paper studies the limits of a spatial random field generated by uniformly scattered random sets, as the density lambda of the sets grows to infinity and the mean volume rho of the sets tends to zero. Assuming that the volume distribution has a regularly varying tail with infinite variance, we show that the centered and renormalized random field can have three different limits, depending on the relative speed at which lambda and rho are scaled. If lambda grows much faster than rho shrinks,...
-
作者：Aldous, David
作者单位：University of California System; University of California Berkeley
摘要：Consider routing traffic on the N x N torus, simultaneously between all source-destination pairs, to minimize the cost Sigma e c(e)f(2) (e), where f (e) is the volume of flow across edge e and the c(e) form an i.i.d. random environment. We prove existence of a rescaled N -> infinity limit constant for minimum cost, by comparison with an appropriate analogous problem about minimum-cost flows across a M x M subsquare of the lattice.
-
作者：Benjamini, Itai; Gurel-Gurevich, Ori; Lyons, Russell
作者单位：Weizmann Institute of Science; Indiana University System; Indiana University Bloomington
摘要：We show that the edges crossed by a random walk in a network form a recurrent graph a.s. In fact, the same is true when those edges are weighted by the number of crossings.
-
作者：El Karoui, Noureddine
作者单位：University of California System; University of California Berkeley
摘要：We consider the asymptotic fluctuation behavior of the largest eigenvalue of certain sample covariance matrices in the asymptotic regime where both dimensions of the corresponding data matrix go to infinity. More precisely, let X be an n x p matrix, and let its rows be i.i.d. complex normal vectors with mean 0 and covariance Sigma p. We show that for a large class of covariance matrices Sigma P, the largest eigenvalue of X*X is asymptotically distributed (after recentering and rescaling) as th...
-
作者：Yang, Ming
作者单位：Columbia University
摘要：Let X-t be any additive process in R-d. There are finite indices delta(i), beta(i), i = 1. 2 and a function u, all of which are defined in terms of the characteristics of X-t, such that lim(t -> 0) inf u(t)X--1/n(t)* = {0, if n > delta(1), {infinity, if n < delta(2), lim(t -> 0) sup u(t)X--1/n(t)* = {0, if n > beta(2), a.s., {infinity, if n < beta(1), where X-t(*) = sup(0 < s < t) |X-s|. When X-t is a Levy process with X-0 = 0, delta 1 = delta 2, beta 1 = beta 2 and u(t) = t. This is a special...
-
作者：Gaertner, Juergen; Koenig, Wolfgang; Molchanov, Stanislav
作者单位：Technical University of Berlin; University of North Carolina; University of North Carolina Charlotte; Leipzig University
摘要：We consider the parabolic Anderson problem partial derivative(t)u = Delta u + xi(x)u on R+ x Z(d) with localized initial condition u (0, x) = delta(0)(x) and random i.i.d. potential xi. Under the assumption that the distribution of xi(0) has a double-exponential, or slightly heavier, tail, we prove the following geometric characterization of intermittency: with probability one, as t -> infinity, the over-whelming contribution to the total mass Sigma x u(t, x) comes from a slowly increasing num...
-
作者：Bojdecki, Tomasz; Gorostiza, Luis G.; Talarczyk, Anna
作者单位：University of Warsaw; University of Warsaw
摘要：We prove a functional limit theorem for the resealed occupation time fluctuations of a (d, alpha, beta)-branching particle system [particles moving in R-d according to a symmetric alpha-stable Levy process, branching law in the domain of attraction of a (1+ beta)-stable law, 0 < beta < 1, uniform Poisson initial state] in the case of intermediate dimensions, alpha / beta < d < alpha (1+ beta) / beta. The limit is a process of the form K gimel xi, where K is a constant, gimel is the Lebesgue me...
-
作者：Sezer, Deniz
作者单位：York University - Canada
摘要：We develop the mathematics of a filtration shrinkage model that has recently been considered in the credit risk modeling literature. Given a finite collection of points x(1) < ... < x(N) in R, the region indicator function R(x) assumes the value i if x is an element of (x(i - 1), x(i)]. We take F to be the filtration generated by (R(X-t))(t >= 0), where X is a diffusion with infinitesimal generator A. We prove a martingale representation theorem for F in terms of stochastic integrals with resp...
-
作者：Berti, Patrizia; Rigo, Pietro
作者单位：Universita di Modena e Reggio Emilia; University of Pavia
摘要：Let (ohm, B, P) be a probability space, A subset of B a sub-alpha-field, and mu a regular conditional distribution for P given A. Necessary and sufficient conditions for mu (w) (A) to be 0-1, for all A is an element of A and w is an element of A(0), where A(0) is an element of A and P(A(0)) = 1, are given. Such conditions apply, in particular, when A is a tail sub-alpha-field. Let H(w) denote the A-atom including the point w is an element of ohm. Necessary and sufficient conditions for mu(w) (...
-
作者：Roy, Emmanuel
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris 13
摘要：We show that a stationary IDp process (i.e., an infinitely divisible stationary process without Gaussian part) can be written as the independent sum of four stationary IDp processes, each of them belonging to a different class characterized by its Levy measure. The ergodic properties of each class are, respectively, nonergodicity, weak mixing, mixing of all order and Bernoullicity. To obtain these results, we use the representation of an IDp process as an integral with respect to a Poisson mea...
