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作者：Aurzada, Frank; Dereich, Steffen
作者单位：Technical University of Berlin
摘要：We study the small deviation problem logP(sup(t is an element of[0,1]) vertical bar X-t vertical bar <= epsilon), as epsilon -> 0, for general Levy processes X. The techniques enable us to determine the asymptotic rate for general real-valued Levy processes, which we demonstrate with many examples. As a particular consequence, we show that a Levy process with nonvanishing Gaussian component has the same (strong) asymptotic small deviation rate as the corresponding Brownian motion.
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作者：Giacomin, Giambattista; Toninelli, Fabio Lucio
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS)
摘要：Recent results have lead to substantial progress in understanding the role of disorder in the (de)localization transition of polymer pinning models. Notably, there is an understanding of the crucial issue of disorder relevance and irrelevance that is now rigorous. In this work, we exploit interpolation and replica coupling methods to obtain sharper results on the irrelevant disorder regime of pinning models. In particular, in this regime, we compute the first order term in the expansion of the...
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作者：Getoor, Ronald
作者单位：University of California System; University of California San Diego
摘要：During the three decades from 1930 to 1960 J. L. Doob was, with the possible exception of Kolmogorov, the man most responsible for the transformation of the study of probability to a mathematical discipline. His accomplishments were recognized by both probabilists and other mathematicians in that he is the only person ever elected to serve as president of both the IMS and the AMS. This article is an attempt to discuss his contributions to two areas in which his work was seminal, namely, the fo...
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作者：Angel, Omer; Holroyd, Alexander; Romik, Dan
作者单位：University of British Columbia; Microsoft; Hebrew University of Jerusalem
摘要：Particles labelled 1,..., n are initially arranged in increasing order. Subsequently, each pair of neighboring particles that is currently in increasing order swaps according to a Poisson process of rate 1. We analyze the asymptotic behavior of this process as n -> infinity. We prove that the space-time trajectories of individual particles converge (when suitably scaled) to a certain family of random curves with two points of non-differentiability, and that the permutation matrix at a given ti...
