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作者：Fernique, X
作者单位：Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
摘要：Let G be a Gaussian vector taking its values in a separable Frechet space E. We denote by gamma its law and by (H, parallel to(.)parallel to) its reproducing Hilbert space. Moreover, let X be an E-valued random vector of law mu. In the first section, we prove that if mu is absolutely continuous relative to gamma, then there exist necessarily a Gaussian vector G' of law gamma and an H-valued random vector Z such that G' + Z has the law mu of X. This fact is a direct consequence of concentration...
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作者：Durrett, R; Limic, V
作者单位：Cornell University; University of British Columbia
摘要：Motivated by the problem of the evolution of DNA sequences, Kauffman and Levin introduced a model in which fitnesses were assigned to strings of 0's and 1's of length N based on the values observed in a sliding window of length K + 1. When K greater than or equal to 1, the landscape is quite complicated with many local maxima. Its properties have been extensively investigated by simulation but until our work and the independent investigations of Evans and Steinsaltz little was known rigorously...
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作者：Keane, M; Steif, JE
作者单位：Wesleyan University; University of Amsterdam; Chalmers University of Technology; University System of Georgia; Georgia Institute of Technology
摘要：We show that there is a finitary isomorphism from a finite state independent and identically distributed (i.i.d.) process to the T, T-1 process associated to one-dimensional random walk with positive drift. This contrasts with the situation for simple symmetric random walk in any dimension, where it cannot be a finitary factor of any i.i.d. process, including in d greater than or equal to 5, where it becomes weak Bernoulli.
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作者：De Jeu, M
作者单位：Leiden University; Leiden University - Excl LUMC
摘要：We prove in a direct fashion that a multidimensional probability measure mu is determinate if the higher-dimensional analogue of Carleman's condition is satisfied. In that case, the polynomials, as well as certain proper subspaces of the trigonometric functions, are dense in all associated L-p-spaces for 1 less than or equal to p < infinity. In particular these three statements hold if the reciprocal of a quasi-analytic weight has finite integral under mu. We give practical examples of such we...
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作者：Limic, V
作者单位：University of British Columbia
摘要：Using martingale techniques and comparison with the generalized Urn scheme, it is shown that the edge reinforced random walk on a graph of bounded degree, with the weight function W(k) = k(rho), rho > 1, traverses (crosses) a random attracting edge at all large times. If the graph is a triangle, the above result is in agreement with a conjecture of Sellke.
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作者：Giné, E; Mason, DM; Zaitsev, AY
作者单位：University of Connecticut; University of Delaware; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences
摘要：The notion of an L-1-norm density estimator process indexed by a class of kernels is introduced. Then a functional central limit theorem and a Glivenko-Cantelli theorem are established for this process. While assembling the necessary machinery to prove these results, a body of Poissonization techniques and restricted chaining methods is developed, which is useful for studying weak convergence of general processes indexed by a class of functions. None of the theorems imposes any condition at al...
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作者：Jacod, J; Jakubowski, A; Mémin, J
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite; Nicolaus Copernicus University; Universite de Rennes
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作者：Jajte, R
作者单位：University of Lodz
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作者：Gordon, Y; Litvak, A; Schütt, C; Werner, E
作者单位：Technion Israel Institute of Technology; University of Kiel; University System of Ohio; Case Western Reserve University
摘要：Let f(i), i = 1, n, be copies of a random variable f and let N be an Orlicz function. We show that for every x is an element of R-n the expectation Eparallel to(x(i)f(i))(i=1)(n)parallel to(N) is maximal (up to an absolute constant) if f(i), i = 1,...,n, are independent. In that case we show that the expectation Eparallel to(x(i) f(i))(i = 1)(n)parallel to(N) is equivalent to parallel toxparallel to(M), for some Orlicz function M depending on N and on distribution of f only. We provide applica...
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作者：Pra, PD; Paganoni, AM; Posta, G
作者单位：Polytechnic University of Milan
摘要：We consider nonconservative, reversible spin systems, with unbounded discrete spins. We show that for a class of these dynamics in a high temperature regime, the relative entropy with respect to the equilibrium distribution decays exponentially in time, although the logarithmic-Sobolev inequality fails. To this end we prove a weaker modification of the logarithmic-Sobolev inequality.
