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作者：Bourgade, P.
作者单位：Sorbonne Universite
摘要：We give a probabilistic proof of the Weyl integration formula on U(n), the unitary group with dimension it. This relies on a suitable definition of Haar measures conditioned to the existence of a stable subspace with any given dimension p. The developed method leads to the following result: for this conditional measure, writing Z(U)((p)) for the first nonzero derivative of the characteristic polynomial at 1, Z(U)((p))/p! =(law) Pi(n-p)(l=1)(1-X(l)), the X(l)'s being explicit independent random...
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作者：Fey, Anne; Meester, Ronald; Redig, Frank
作者单位：Vrije Universiteit Amsterdam; Leiden University; Leiden University - Excl LUMC
摘要：We study the sandpile model in infinite volume on Z(d). In particular, we are interested in the question whether or not initial configurations, chosen according to a stationary measure mu, are mu-almost surely stabilizable. We prove that stabilizability does not depend on the particular procedure of stabilization we adopt. In d = 1 and mu a product measure with density rho = 1 (the known critical value for stabilizability in d = 1) with a positive density of empty sites, we prove that mu is no...
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作者：Spakulova, Iva
作者单位：Vanderbilt University
摘要：This article presents a method for finding the critical probability pc for the Bernoulli bond percolation on graphs with the so-called tree-like structure. Such a graph can be decomposed into a tree of pieces, each of which has finitely many isomorphism classes. This class of graphs includes the Cayley graphs of amalgamated products, HNN extensions or general groups acting on trees. It also includes all transitive graphs with more than one end. The idea of the method is to find a multi-type Ga...
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作者：Bertoin, Jean
作者单位：Sorbonne Universite; Universite PSL; Ecole Normale Superieure (ENS)
摘要：We consider a (sub-)critical Galton-Watson process with neutral mutations (infinite alleles model), and decompose the entire population into clusters of individuals carrying the same allele. We specify the law of this allelic partition in terms of the distribution of the number of clone-children and the number of mutant-children of a typical individual. The approach combines an extension of Harris representation of Galton-Watson processes and a version of the ballot theorem. Some limit theorem...
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作者：Kabluchko, Zakhar; Schlather, Martin; de Haan, Laurens
作者单位：University of Gottingen; Erasmus University Rotterdam - Excl Erasmus MC; Erasmus University Rotterdam
摘要：Let W-i, i is an element of N, be independent copies of a zero-mean Gaussian process {W (t), t is an element of R-d} with stationary increments and variance sigma(2)(t). Independently of W-i, let Sigma(infinity)(i=1) U-delta(i) be a Poisson point process on the real line with intensity e(-y) dy. We show that the law of the random family of functions {V-i(.), i is an element of N}, where V-i(t) = U-i + W-i(t) - sigma(2)(t)/2, is translation invariant. In particular, the process n(t) = V-i=1(inf...
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作者：Sznitman, Alain-Sol
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We study the asymptotic behavior for large N of the disconnection time T(N) of a simple random walk on the discrete cylinder (Z/NZ)(d) x Z, when d >= 2. We explore its connection with the model of random interlacements on Z(d+1) recently introduced in [Ann. Math., in press], and specifically with the percolative properties of the vacant set left by random interlacements. As an application we show that in the large N limit the tail of T(N)/N(2d) is dominated by the tail of the first time when t...
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作者：Bentkus, Vidmantas; Jing, Bing-Yi; Zhou, Wang
作者单位：Vilnius University; Hong Kong University of Science & Technology; National University of Singapore
摘要：Let X-1, ..., X-n be i.i.d. random observations. Let S = L + T be a U-statistic of order k >= 2 where L is a linear statistic having asymptotic normal distribution, and T is a stochastically smaller statistic. We show that the rate of convergence to normality for S can be simply expressed as the rate of convergence to normality for the linear part L plus a correction term, (varT) ln(2) (varT), under the condition ET2 < infinity. An optimal bound without this log factor is obtained under a lowe...
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作者：Bramson, Maury; Zeitouni, Ofer
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Weizmann Institute of Science
摘要：In this paper we study the tightness of solutions for a family of recursion equations. These equations arise naturally in the study of random walks on tree-like structures. Examples include the maximal displacement of a branching random walk in one dimension and the cover time of a symmetric simple random walk on regular binary trees. Recursion equations associated with the distribution functions of these quantities have been used to establish weak laws of large numbers. Here, we use these rec...
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作者：Hochman, Michael
作者单位：Hebrew University of Jerusalem
摘要：For arrays (S(i, j))(1 <= i <= j) of random variables that are stationary in an appropriate sense, we show that the fluctuations of the process (S(l, n))(n=1)(infinity) can be bounded in terms of a measure of the mean subadditivity of the process (S(i, j))(1 <= i <= j). We derive universal upcrossing inequalities with exponential decay for Kingman's subadditive ergodic theorem, the Shannon-MacMillan-Breiman theorem and for the convergence of the Kolmogorov complexity of a stationary sample.
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作者：Reinert, Gesine; Roellin, Adrian
作者单位：University of Oxford; National University of Singapore
摘要：In this paper we establish a multivariate exchangeable pairs approach within the framework of Stein's method to assess distributional distances to potentially singular multivariate normal distributions. By extending the statistics into a higher-dimensional space, we also propose an embedding method which allows for a normal approximation even when the corresponding statistics of interest do not lend themselves easily to Stein's exchangeable pairs approach. To illustrate the method, we provide ...
