-
作者：Gravner, J; Griffeath, D
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：In the threshold growth model on an integer lattice, the occupied set grows according to a simple local rule: a site becomes occupied iff it sees at least a threshold number of already occupied sites in its prescribed neighborhood In this paper, we analyze the behavior of two-dimensional threshold growth dynamics started from a sparse Bernoulli density of occupied sites. We explain how nucleation of rare centers, invariant shapes and interaction between growing droplets influence the first pas...
-
作者：Pinsky, RG
摘要：We consider the supercritical finite measure-valued diffusion, X(t), whose log-laplace equation is associated with the semilinear equation u(t) = Lu + beta u - alpha u(2), where alpha, beta > 0, and L = 1/2 Sigma(i,j=1)(d) alpha(ij) (partial derivative(2)/(partial derivative x(i) partial derivative x(j))) + Sigma(i=1)(d) b(i) (partial derivative/partial derivative x(i)). A path X(.) is said to survive if X(t) not equal 0, for all t greater than or equal to 0. Since beta > 0, P-mu(X(.) survives...
-
作者：Fukai, Y; Uchiyama, K
摘要：It is proved that the potential kernel of a recurrent, aperiodic random walk on the integer lattice Z(2) admits an asymptotic expansion of the form (2 pi root\Q\)(-1)ln Q(x(2), - x(1)) + const + \x\U--1(1)(omega(x)) + \x\U--2(2)(omega(2)) + ..., where \Q\ and Q(theta) are, respectively, the determinant and the quadratic form of the covariance matrix of the increment X of the random walk, omega(2) = x/\x\ and the U-h(omega) are smooth functions of omega, \omega\ = 1, provided that all the momen...
-
作者：Toth, B
作者单位：University of Zurich; Heriot Watt University; Centrum Wiskunde & Informatica (CWI)
摘要：We consider non-Markovian, self-interacting random walks (SIRW) on the one-dimensional integer lattice. The walk starts from the origin and at each step jumps to a neighboring site. The probability of jumping along a bond is proportional to w (number of previous jumps along that lattice bond), where w:N --> R(+) is a monotone weight function. Exponential and subexponential weight functions were considered in earlier papers. In the present paper we consider weight functions w with polynomial as...
-
作者：Doney, RA
摘要：A rather complicated condition is shown to be necessary and sufficient for a Levy process to have points of increase. A much simpler condition is then shown to be sufficient in the general case, and necessary under certain regularity conditions. The approach used here also gives a unified proof of results for certain special classes of Levy processes, which have previously been obtained by Bertoin.
-
作者：Bentkus, V; Gotze, F
摘要：We prove the Berry-Esseen bound for the Student t-statistic. Under the assumption of a third moment this bound coincides (up to an absolute constant) with the classical Berry-Esseen bound for the mean. In general the distribution of the Student statistic converges to the standard normal distribution function at least as fast as the distribution of the mean, and sometimes faster. For example, rates of convergence can be proved if the underlying distribution is in the domain of attraction of the...
-
作者：Rosinski, J; Samorodnitsky, G
作者单位：Cornell University
摘要：We consider stochastic processes X = {X(t), t is an element of T} represented as a Levy chaos of finite order, that is, as a finite sum of multiple stochastic integrals with respect to a symmetric infinitely divisible random measure. For a measurable subspace V of RT We prove a very general zero-one law P(X is an element of V) = 0 or 1, providing a complete analog to the corresponding situation in the case of symmetric infinitely divisible processes (single integrals with respect to an infinit...
-
作者：Alexander, KS
摘要：Every two-dimensional incompressible flow follows the level lines of some scalar function psi on R(2); transport properties of the flow depend in part on whether all level lines are bounded. We study the structure of the level lines when psi is a stationary random held. We show that under mild hypotheses there is only one possible alternative to bounded level lines: the ''treelike'' random fields, which, for some interval of values of a, have a unique unbounded level line at each level a, with...
-
作者：Landim, C; Sethuraman, S; Varadhan, S
作者单位：New York University
摘要：We give a lower bound on the spectral gap for symmetric zero-range processes. Under same conditions on the rate function, we show that the gap shrinks as n(-2) independent of the density, for the dynamics localized on a cube of size n(d). We follow the method outlined by Lu and Yau, where a similar spectral gap is proved for Kawasaki dynamics.
-
作者：Stacey, AM
摘要：Let T-d be a homogeneous tree in which every vertex has d neighbors. A new proof is given that the contact process on T-d exhibits two phase transitions when d greater than or equal to 3, a behavior which distinguishes it from the contact process on Z(n). This is the first proof which does not involve calculation of bounds on critical values, and it is much shorter than the previous proof for the binary tree, T-3. The method is extended to prove the existence of an intermediate phase for a mor...
