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作者：Arguin, Louis-Pierre; Bovier, Anton; Kistler, Nicola
作者单位：Universite de Montreal; University of Bonn
摘要：We prove that the extremal process of branching Brownian motion, in the limit of large times, converges weakly to a cluster point process. The limiting process is a (randomly shifted) Poisson cluster process, where the positions of the clusters is a Poisson process with intensity measure with exponential density. The law of the individual clusters is characterized as branching Brownian motions conditioned to perform unusually large displacements, and its existence is proved. The proof combines...
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作者：Gordina, Maria; Melcher, Tai
作者单位：University of Connecticut; University of Virginia
摘要：Let G denote an infinite-dimensional Heisenberg-like group, which is a class of infinite-dimensional step 2 stratified Lie groups. We consider holomorphic functions on G that are square integrable with respect to a heat kernel measure which is formally subelliptic, in the sense that all appropriate finite-dimensional projections are smooth measures. We prove a unitary equivalence between a subclass of these square integrable holomorphic functions and a certain completion of the universal envel...
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作者：Bordenave, Charles; Guionnet, Alice
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：Consider an Hermitian random matrix with, above the diagonal, independent entries with -stable symmetric distribution and . We establish new bounds on the rate of convergence of the empirical spectral distribution of this random matrix as goes to infinity. When and , we give vanishing bounds on the -norm of the eigenvectors normalized to have unit -norm. On the contrary, when , we prove that these eigenvectors are localized.
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作者：Alsmeyer, Gerold; Meiners, Matthias
作者单位：University of Munster; Uppsala University
摘要：Given a sequence (C, T) = (C, T (1), T (2), . . .) of real-valued random variables with T (j) a parts per thousand yen 0 for all j a parts per thousand yen 1 and almost surely finite N = sup{j a parts per thousand yen 1 : T (j) > 0}, the smoothing transform associated with (C, T), defined on the set of probability distributions on the real line, maps an element to the law of , where X (1), X (2), . . . is a sequence of i.i.d. random variables independent of (C, T) and with distribution P. We s...
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作者：Chistyakov, G. P.; Goetze, F.
作者单位：University of Bielefeld; National Academy of Sciences Ukraine; B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine
摘要：We prove Edgeworth type expansions for distribution functions of sums of free random variables under minimal moment conditions. The proofs are based on the analytic definition of free convolution.
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作者：van den Berg, J.; Gandolfi, A.
作者单位：Centrum Wiskunde & Informatica (CWI); Vrije Universiteit Amsterdam; University of Florence
摘要：Recently, van den Berg and Jonasson gave the first substantial extension of the BK inequality for non-product measures: they proved that, for -out-of- measures, the probability that two increasing events occur disjointly is at most the product of the two individual probabilities. We show several other extensions and modifications of the BK inequality. In particular, we prove that the antiferromagnetic Ising Curie-Weiss model satisfies the BK inequality for all increasing events. We prove that ...
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作者：Greven, Andreas; Pfaffelhuber, Peter; Winter, Anita
作者单位：University of Erlangen Nuremberg; University of Freiburg; University of Duisburg Essen
摘要：The measure-valued Fleming-Viot process is a diffusion which models the evolution of allele frequencies in a multi-type population. In the neutral setting the Kingman coalescent is known to generate the genealogies of the individuals in the population at a fixed time. The goal of the present paper is to replace this static point of view on the genealogies by an analysis of the evolution of genealogies. We encode the genealogy of the population as an (isometry class of an) ultra-metric space wh...
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作者：Eberle, Andreas; Marinelli, Carlo
作者单位：University of Bonn; Free University of Bozen-Bolzano
摘要：We study approximations of evolving probability measures by an interacting particle system. The particle system dynamics is a combination of independent Markov chain moves and importance sampling/resampling steps. Under global regularity conditions, we derive non-asymptotic error bounds for the particle system approximation. In a few simple examples, including high dimensional product measures, bounds with explicit constants of feasible size are obtained. Our main motivation are applications t...
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作者：Rider, Brian; Sinclair, Christopher D.; Xu, Yuan
作者单位：University of Colorado System; University of Colorado Boulder; University of Oregon
摘要：We consider an ensemble of interacting charged particles on the line consisting of two species of particles with charge ratio 2:1 in the presence of an external field. With the total charge fixed and the system held at temperature corresponding to beta = 1, it is proved that the particles form a Pfaffian point process. When the external field is quadratic (the harmonic oscillator potential), we produce the explicit family of skew-orthogonal polynomials necessary to simplify the related matrix ...
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作者：Chatterjee, Sourav; Dey, Partha S.
作者单位：New York University
摘要：We prove that first-passage percolation times across thin cylinders of the form [0, n] x [-h (n) , h (n) ] (d-1) obey Gaussian central limit theorems as long as h (n) grows slower than n (1/(d+1)). It is an open question as to what is the fastest that h (n) can grow so that a Gaussian CLT still holds. Under the natural but unproven assumption about existence of fluctuation and transversal exponents, and strict convexity of the limiting shape in the direction of (1, 0, . . . , 0), we prove that...
