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作者：Asselah, A; Pra, PD
作者单位：Aix-Marseille Universite; Polytechnic University of Milan
摘要：We study quasi-stationary measures for conservative particle systems in the infinite lattice. Existence of quasi-stationary measures is established for a fairly general class of reversible systems. For the special cases of a system of independent random walks and the symmetric simple exclusion process, it is shown that qualitative features of quasi-stationary measures change drastically with dimension.
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作者：Bertoin, J
作者单位：Universite Paris Cite; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Aldous and Pitman have studied the asymptotic behavior of the additive coalescent processes using a nested family random forests: derived by logging certain inhomogeneous continuum random trees. Here we propose a different approach based on partitions of the unit inter val induced by certain bridges with exchangeable increments. The analysis is made simple by an interpretation in terms of an aggregating server system.
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作者：Fill, JA; Machida, M
作者单位：Johns Hopkins University; Utah System of Higher Education; Utah State University
摘要：We explore and relate two notions of monotonicity, stochastic and realizable, for a system of probability measures on a common finite partially ordered set (poset) f when the measures are indexed by another poset A. We give counterexamples to show that the two notions are not always equivalent, but for various large classes of f we also present conditions on the poset A that are necessary and sufficient for equivalence. When A = f the condition that the cover graph of f have no cycles is neces...
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作者：Stephenson, D
作者单位：Cornell University
摘要：We consider an interacting random walk on Z (d) where particles interact only at times when a particle jumps to a site at which there are at least n - 1 other particles present. If there are i greater than or equal to n - 1 particles present, then the particle coalesces (is removed from the system) with probability ci and annihilates (is removed along with another particle) with probability ai. We call this process the n-threshold randomly coalescing and annihilating random walk. We show that,...
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作者：Bolthausen, E; Deuschel, JD; Giacomin, G
作者单位：University of Zurich; Technical University of Berlin; Universite Paris Cite
摘要：We consider the lattice version of the free field in two dimensions (also called harmonic crystal). The main aim of the paper is to discuss quantitatively the entropic repulsion of the random surface in the presence of a hard wall. The basic ingredient of the proof is the analysis of the maximum of the field which requires a multiscale analysis reducing the problem essentially to a problem on a field with a tree structure.
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作者：Fernández, R; Ferrari, PA; Garcia, NL
作者单位：Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidade de Sao Paulo; Universidade Estadual de Campinas
摘要：We present a probabilistic approach for the study of systems with exclusions in the regime traditionally studied via cluster-expansion methods. In this paper we focus on its application for the gases of Peierls contours found in the study of the Ising model at low temperatures, but most of the results are general. We realize the equilibrium measure as the invariant measure of a loss network process whose existence is ensured by a subcriticality condition of a dominant branching process. In thi...
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作者：Karatzas, I; Sudderth, WD
作者单位：Columbia University; Columbia University; University of Minnesota System; University of Minnesota Twin Cities
摘要：Consider a process X(.) = {X(t), 0 less than or equal to t less than or equal to infinity) with values in the interval I = (0, 1), absorption at the boundary points of I, and dynamics dX(t) =beta(t) dt + sigma(t) dW(t), X(0) = x. The values beta(t), sigma(t)) are selected by a controller from a subset of 91 x (0, infinity) that depends on the current position X(t), for every t greater than or equal to 0. At any stopping rule tau of his choice, a second player, called a stopper, can halt the ev...
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作者：Janvresse, E
作者单位：Universite de Rouen Normandie
摘要：We consider a random walk on Sn-1, the standard sphere of dimension n -1, generated by random rotations on randomly selected coordinate planes i, j with 1 less than or equal to i < j less than or equal to n. This dynamic was used by Marc Kac as a model for the spatially homogeneous Boltzmann equation. We prove that the spectral gap on Sn-1 is n(-1) up to a constant independent of n.
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作者：Driver, BK; Srimurthy, VK
作者单位：University of California System; University of California San Diego
摘要：Let t > 0, K be a connected compact Lie group equipped with an Ad(K) - invariant inner product on the Lie Algebra of K. Associated to this data are two measures mu (0)(t) and nu (0)(t) on L(K) - the space of continuous loops based at e is an element of K. The measure mu (0)(t) is pinned Wiener measure with variance t while the measure nu (0)(t) is a heat kernel measure on L(K). The measure mu (0)(t) is constructed using a K - valued Brownian motion while the measure nu (0)(t) is constructed us...
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作者：Bañuelos, R; DeBlassie, RD; Smits, R
作者单位：Purdue University System; Purdue University; Texas A&M University System; Texas A&M University College Station; University System of Maryland; Towson University
摘要：Let D be the interior of a parabola in R-2 and T (D) the first exit time of Brownian motion from D. We show - log P(T-D > t) behaves like t(1/3) as t --> infinity.
