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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：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：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.
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作者：Groeneboom, P
作者单位：Delft University of Technology; Vrije Universiteit Amsterdam
摘要：Let L-n be the length of the longest increasing subsequence of a random permutation of the numbers 1,..., n, for the uniform distribution on the set of permutations. Hammersley's interacting particle process, implicit in Hammersley (1972), has been used in Aldous and Diaconis (1995) to provide a soft hydrodynamical argument for proving that lim(n --> infinity) ELn/rootn = 2. We show in this note that the latter result is in fact an immediate consequence of properties of a random 2-dimensional ...
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作者：Atar, R; Budhiraja, A; Dupuis, P
作者单位：Technion Israel Institute of Technology; University of North Carolina; University of North Carolina Chapel Hill; Brown University
摘要：Let G subset of R-k be a convex polyhedral cone with vertex at the origin given as the intersection of half spaces {G(i), i = 1,..., N} where n(i) and d(i) denote the inward normal and direction of constraint associated with G(i), respectively. Stability properties of a class of diffusion processes, constrained to take values in G, are studied under the assumption that the Skorokhod problem defined by the data {(n(i), d(i)), i = 1,..., N} is well posed and the Skorokhod map is Lipschitz contin...
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作者：Fleischmann, K; Xiong, J
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Tennessee System; University of Tennessee Knoxville
摘要：In generalization of the mutually catalytic super-Brownian motion in R of Dawson and Perkins and Mytnik, a function-valued cyclically catalytic model X is constructed as a strong Markov solution to a martingale problem. Starting with a finite population X-0, each pair of neighboring types will globally segregate in the long-term limit (noncoexistence of neighboring types). Also finer extinction-survival properties depending on X-0 are studied in the spirit of Mueller and Perkins. In fact, X-0 ...
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作者：Howard, CD; Newman, CM
作者单位：City University of New York (CUNY) System; Baruch College (CUNY); New York University
摘要：The metric D-alpha(q, q ') on the set Q of particle locations of a homogeneous Poisson process on R-d, defined as the infimum of (Sigmai \q(i) - q(i+1)\ (alpha))(1/alpha) over sequences in Q starting with q and ending with q ' (where \ (.)\ denotes Euclidean distance) has nontrivial geodesics when alpha > 1. The cases 1 < alpha < infinity are the Euclidean first-passage percolation (FPP) models introduced earlier by the authors, while the geodesics in the case alpha = infinity are exactly the ...
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作者：Zegarlinski, B
作者单位：Imperial College London
摘要：We show that a strong mixing condition implies a Bakry-Bobkov-Ledoux inequality for a probability measure on infinite-dimensional space.
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作者：Jonasson, J
作者单位：University of Gothenburg; Chalmers University of Technology
摘要：We consider a version of the Boolean (or Poisson blob) continuum percolation model where, at each point of a Poisson point process in the Euclidean plane with intensity lambda, a copy of a given compact convex set A with fixed rotation is placed. To each A we associate a critical value lambda (c)(A) which is the infimum of intensities lambda for which the occupied component contains an unbounded connected component. It is shown that min{lambda (c)(A) : A convex of area a} is attained if A is a...
