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作者：Fulman, Jason
作者单位：University of Southern California
摘要：It is shown that the combinatorics of commutation relations is well suited for analyzing the convergence rate of certain Markov chains. Examples studied include random walk on irreducible representations, a local random walk on partitions whose stationary distribution is the Ewens distribution, and some birth-death chains.
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作者：Cerrai, Sandra; Freidlin, Mark
作者单位：University of Florence; University System of Maryland; University of Maryland College Park
摘要：We consider the averaging principle for stochastic reaction-diffusion equations. Under some assumptions providing existence of a unique invariant measure of the fast motion with the frozen slow component, we calculate limiting slow motion. The study of solvability of Kolmogorov equations in Hilbert spaces and the analysis of regularity properties of solutions, allow to generalize the classical approach to finite-dimensional problems of this type in the case of SPDE's.
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作者：Ford, Kevin
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：We give sharp, uniform estimates for the probability that a random walk of n steps on the reals avoids a half-line [y, infinity) given that it ends at the point x. The estimates hold for general continuous or lattice distributions provided the fourth moment is finite.
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作者：Morters, Peter; Shieh, Narn-Rueih
作者单位：University of Bath; National Taiwan University
摘要：Let D subset of R-3 be the set of double points of a three-dimensional Brownian motion. We show that, if xi = xi 3(2, 2) is the intersection exponent of two packets of two independent Brownian motions, then almost surely, the phi-packing measure of D is zero if integral(0+) r(-1-xi)phi(r)(xi) dr < infinity, and infinity otherwise. As an important step in the proof we show up-to-constants estimates for the tail at zero of Brownian intersection local times in dimensions two and three.
