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作者：Asselah, Amine; Ferrari, Pablo A.
作者单位：Aix-Marseille Universite; Universidade de Sao Paulo
摘要：We consider a system of asymmetric independent random walks on Z(d), denoted by {eta(t), t is an element of R}, stationary under the product Poisson measure v(rho) of marginal density p > 0. We fix a pattern A, an increasing local event, and denote by tau the hitting time of A. By using a loss network representation of our system, at small density, we obtain a coupling between the laws of eta(t) conditioned on (tau > t) for all times t. When d >= 3, this provides bounds on the rate of converge...
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作者：Conger, Mark; Viswanath, D.
作者单位：University of Michigan System; University of Michigan
摘要：By a well-known result of Bayer and Diaconis, the maximum entropy model of the common riffle shuffle implies that the number of riffle shuffles necessary to mix a standard deck of 52 cards is either 7 or 11-with the former number applying when the metric used to define mixing is the total variation distance and the latter when it is the separation distance. This and other related results assume all 52 cards in the deck to be distinct and require all 52! permutations of the deck to be almost eq...
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作者：Jiang, Tiefeng
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We solve an open problem of Diaconis that asks what are the largest orders of p(n) and q(n) such that Z(n), the p(n) x q(n) upper left block of a random matrix Gamma(n) which is uniformly distributed on the orthogonal group O(n), can be approximated by independent standard normals? This problem is solved by two different approximation methods. First, we show that the variation distance between the joint distribution of entries of Z(n) and that of p(n)q(n) independent standard normals goes to z...
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作者：Dalang, Robert C.; Mueller, C.; Zambotti, L.
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of Rochester; Polytechnic University of Milan
摘要：We study the hitting properties of the solutions u of a class of parabolic stochastic partial differential equations with singular drifts that prevent u from becoming negative. The drifts can be a reflecting term or a nonlinearity cu(-3), with c > 0. We prove that almost surely, for all time t > 0, the solution ut hits the level 0 only at a finite number of space points, which depends explicitly on c. In particular, this number of hits never exceeds 4 and if c > 15/8, then level 0 is not hit.
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作者：Sheffield, Scott
作者单位：University of California System; University of California Berkeley
摘要：An essential spanning forest of an infinite graph G is a spanning forest of G in which all trees have infinitely many vertices. Let G(n) be an increasing sequence of finite connected subgraphs of G for which boolean OR G(n) = G. Pemantle's arguments imply that the uniform measures on spanning trees of G, converge weakly to an Aut(G)-invariantmeasure mu(G) on essential spanning forests of G. We show that if G is a connected, amenable graph and F subset of Aut(G) acts quasitransitively on G, the...
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作者：Hoffman, Christopher; Holroyd, Alexander E.; Peres, Yuval
作者单位：University of Washington; University of Washington Seattle; University of British Columbia; University of California System; University of California Berkeley
摘要：Let Xi be a discrete set in R-d. Call the elements of Xi centers. The well-known Voronoi tessellation partitions R-d into polyhedral regions (of varying sizes) by allocating each site of R-d to the closest center. Here we study fair allocations of R-d to Iota in which the regions allocated to different centers have equal volumes. We prove that if Xi is obtained from a translation-invariant point process, then there is a unique fair allocation which is stable in the sense of the Gale-Shapley ma...
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作者：Cohen, G; Cuny, C
作者单位：Ben-Gurion University of the Negev
摘要：We study random exponential sums of the form Sigma(n)(k=1) X-k exp {i (lambda((1))(k) t(1) +(...)+ lambda((s))(k)t(s))}, where {X-n} is a sequence of random variables and {lambda((i))(n) : 1 <= i <= s} are sequences of real numbers. We obtain uniform estimates (on compact sets) of such sums, for independent centered {X-n} or bounded {X-n} satisfying some mixing conditions. These results generalize recent results of Weber [Math. Inequal. Appl. 3 (2000) 443-457] and Fan and Schneider [Ann. Inst....
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作者：Gaertner, J.; den Hollander, F.
作者单位：Technical University of Berlin; Leiden University; Leiden University - Excl LUMC
摘要：In this paper, we study intermittency for the parabolic Anderson equation partial derivative u/partial derivative t = K Delta u + xi u, where u: Z(d) x [0, infinity) -> R, K is the diffusion constant, Delta is the discrete Laplacian and xi : Z(d) X [0, infinity) -> R is a space-time random medium. We focus on the case where xi is gamma times the random medium that is obtained by running independent simple random walks with diffusion constant rho starting from a Poisson random field with intens...
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作者：Gamburd, Alex
作者单位：University of California System; University of California Santa Cruz
摘要：Brooks and Makover introduced an approach to studying the global geometric quantities (in particular, the first eigenvalue of the Laplacian, injectivity radius and diameter) of a typical compact Riemann surface of large genus based on compactifying finite-area Riemann surfaces associated with random cubic graphs; by a theorem of Belyi, these are dense in the space of compact Riemann surfaces. The question as to how these surfaces are distributed in the Teichmuller spaces depends on the study o...
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作者：Evans, Steven N.; Winter, Anita
作者单位：University of California System; University of California Berkeley; University of Erlangen Nuremberg
摘要：We use Dirichlet form methods to construct and analyze a reversible Markov process, the stationary distribution of which is the Brownian continuum random tree. This process is inspired by the subtree prune and regraft (SPR) Markov chains that appear in phylogenetic analysis. A key technical ingredient in this work is the use of a novel Gromov-Hausdorff type distance to metrize the space whose elements are compact real trees equipped with a probability measure. Also, the investigation of the Di...
