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作者：Fontes, LR; Mathieu, P; Picco, P
作者单位：Universidade de Sao Paulo; Aix-Marseille Universite; Aix-Marseille Universite
摘要：We describe the averaged over the disordered dynamics for the random field Curie-Weiss model. We consider both the magnetization and the full spin dynamics. Our approach is based on spectral asymptotics and includes results on the random fluctuations of eigenvalues and eigenvectors.
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作者：Gärtner, J; König, W
作者单位：Technical University of Berlin
摘要：We consider the parabolic Anderson problem partial derivative (t)u = kappa Deltau + xi (x)u on R+ x R-d with initial condition u(0, x) = 1. Here xi(.) is a random shift-invariant potential having high delta -like peaks on small islands. We express the second-order asymptotics of the pth moment (p is an element of [1, infinity)) of u(t, 0) as t --> infinity in terms of a variational formula involving an asymptotic description of the rescaled shapes of these peaks via their cumulant generating f...
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作者：Baccelli, F; Hong, D
作者单位：Universite PSL; Ecole Normale Superieure (ENS)
摘要：We give an explicit analytic series expansion of the (max, plus)Lyapunov exponent gamma (p) of a sequence of independent and identically distributed random matrices, generated via a Bernoulli scheme depending on a small parameter p. A key assumption is that one of the matrices has a unique normalized eigenvector. This allows us to obtain a representation of this exponent as the mean value of a certain random variable. We then use a discrete analogue of the so-called light-traffic perturbation ...
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作者：Hofmann, N; Müller-Gronbach, T; Ritter, K
作者单位：University of Passau; Free University of Berlin; University of Erlangen Nuremberg
摘要：We analyze the pathwise approximation for systems of stochastic differential equations. The pathwise distance between the solution and its approximation is measured globally on the unit interval in the L-infinity-norm, and we study the expectation of this distance. For systems with additive noise we obtain sharp lower and upper bounds for the minimal error in the class of arbitrary methods which use discrete observations of a Brownian path. The optimal order is achieved by an Euler scheme with...
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作者：Chayes, L; Schonmann, RH
作者单位：University of California System; University of California Los Angeles
摘要：By using mixed percolation as a bridge between site and band percolation, me derive a nem inequality between the critical points of these processes that is optimal in a certain sense, We also extend a result on the crossover exponent of bond-diluted Potts models to site-diluted Potts models. Same new results about the critical line in mixed percolation are also proved.
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作者：Evans, W; Kenyon, C; Peres, Y; Schulman, LJ
作者单位：University of Arizona; Universite Paris Saclay; University of California System; University of California Berkeley; Hebrew University of Jerusalem; University System of Georgia; Georgia Institute of Technology
摘要：Consider a process in which information is transmitted from a given root node on a noisy tree network T. We start with an unbiased random bit R at the root of the tree and send it down the edges of T. On every edge the bit can be reversed with probability epsilon, and these errors occur independently. The goal is to reconstruct R from the values which arrive at the nth level of the tree. This model has been studied in information theory, genetics and statistical mechanics. We bound the reconst...
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作者：Coffman, EG; Flatto, L; Jelenkovic, P
作者单位：Alcatel-Lucent; Lucent Technologies; AT&T; Columbia University
摘要：Starting at time 0, unit-length intervals arrive and are placed on the positive real line by a unit-intensity Poisson process in two dimensions; the left endpoints of intervals appear at the rate of 1 per unit time per unit distance. An arrival is accepted if and only if, for some given x, the interval is contained in [0, x] and overlaps no interval already accepted. This stochastic, on-line interval packing problem generalizes the classical parking problem, the latter corresponding only to th...
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作者：Huebner, M; Lototsky, S
作者单位：Michigan State University; Massachusetts Institute of Technology (MIT)
摘要：In this paper we construct a kernel estimator of a time-varying coefficient of a strongly elliptic partial differential operator in a stochastic parabolic equation. The equation is assumed diagonalizable; that is, all the operators have a common system of eigenfunctions. The mean-square convergence of the estimator is established. The rate of convergence is determined both by the smoothness of the true coefficient and by the asymptotics of the eigenvalues of the operators in the equation.
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作者：Chen, H; Shen, XY
作者单位：University of British Columbia
摘要：This paper derives the strong approximation for a muiticlass queueing network, where jobs after service completion can only move to a downstream service station. Job classes are partitioned into groups. Within a group, jobs are served in the order of arrival; that is, a first-in first-out (FIFO) discipline is in force, and among groups, jobs are served under a preassigned preemptive priority discipline. We obtain the strong approximation for the network through an inductive application of an i...
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作者：Arratia, R; Barbour, AD; Tavaré, S
作者单位：University of Southern California; University of Zurich
摘要：Under very mild conditions, we prove that the number of components in a decomposable logarithmic combinatorial structure has a distribution which is close to Poisson in total variation. The conditions are satisfied for all assemblies, multisets and selections in the logarithmic class. The error in the Poisson approximation is shown under marginally more restrictive conditions to be of exact order O(1/ log n), by exhibiting the penultimate asymptotic approximation; similar results have previous...
