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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：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：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：de Haan, L; Lin, T
作者单位：Erasmus University Rotterdam - Excl Erasmus MC; Erasmus University Rotterdam
摘要：The structure of extreme value distributions in infinite-dimensional space is well known. We characterize the domain of attraction of such extreme-value distributions in the framework of Gine Hahn and Vatan. We intend to use the result for statistical applications.
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作者：Talagrand, M
作者单位：Centre National de la Recherche Scientifique (CNRS)
摘要：We give a reformulation of majorizing measures that does not involve measures, but rather special sequences of partitions. This formulation is more convenient to perform chaining with different distances.
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作者：Tóth, B
作者单位：Budapest University of Technology & Economics
摘要：We prove that, with probability 1, eventually there are no more than three favorite (i.e., most visited) sites of simple symmetric random walks. This partially answers a relatively longstanding question of Erdos and Revesz.
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作者：Benjamini, I; Lyons, R; Peres, Y; Schramm, O
作者单位：Weizmann Institute of Science; Hebrew University of Jerusalem; Indiana University System; Indiana University Bloomington; University of California System; University of California Berkeley
摘要：We study uniform spanning forest measures on infinite graphs. which are weak limits of uniform spanning tree measures from finite subgraphs. These limits can be taken with free (FSF) or wired (WSF) boundary conditions. Pemantle proved that the free and wired spanning forests coincide in Z(d) and that they give a single tree iff d less than or equal to 4. In the present work, we extend Pemantle's alternative to general graphs and exhibit further connections of uniform spanning forests to random...
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作者：Delmas, JF; Dhersin, JS
作者单位：Institut Polytechnique de Paris; Ecole des Ponts ParisTech; Universite Paris Cite
摘要：We present a Kolmogorov's test for the Brownian snake. This result was conjectured by Le Gall in 1998. It has to be compared with Kolmogorov's test for super Brownian motion by Dhersin and Le Gall.
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作者：Pitman, J; Yor, M
作者单位：University of California System; University of California Berkeley; Sorbonne Universite
摘要：The distribution of the sequence of ranked maximum and minimum values attained during excursions of a standard Brownian bridge (B-t(br), 0 less than or equal to t less than or equal to 1) is described. The height M-j(br+) of the jth highest maximum over a positive excursion of the bridge has the same distribution as M-1(br+)/j, where the distribution of Mb(1)(br+) = Sup(0 less than or equal tot less than or equal to1)B(t)(br) is given by Levy's formula P(M-1(br+) > x) = e(-2x2). The probabilit...
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作者：Alexander, KS
作者单位：University of Southern California
摘要：Consider a translation-invariant bond percolation model on the integer lattice which has exponential decay of connectivities, that is, the probability of a connection 0 <----> x by a path of open bonds decreases like exp(-m(theta)\x \) for some positive constant m(theta) which may depend on the direction a = x/\x \. In two and three dimensions, it is shown that if the model has an appropriate mixing property and satisfies a special case of the FKG property, then there is at most a power-law co...
