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作者：Schnellmann, Daniel
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite PSL; Ecole Normale Superieure (ENS)
摘要：We show that for almost every map in a transversal one-parameter family of piecewise expanding unimodal maps the Birkhoff sum of suitable observables along the forward orbit of the turning point satisfies the law of iterated logarithm. This result will follow from an almost sure invariance principle for the Birkhoff sum, as a function on the parameter space. Furthermore, we obtain a similar result for general one-parameter families of piecewise expanding maps on the interval.
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作者：Miller, Jason; Watson, Samuel S.; Wilson, David B.
作者单位：Massachusetts Institute of Technology (MIT); Microsoft; Microsoft
摘要：The conformal loop ensemble with parameter is the canonical conformally invariant measure on countably infinite collections of non-crossing loops in a simply connected domain. We show that the number of loops surrounding an -ball (a random function of and ) minus its expectation converges almost surely as to a random conformally invariant limit in the space of distributions, which we call the nesting field. We generalize this result by assigning i.i.d. weights to the loops, and we treat an alt...
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作者：Cotar, Codina; Kuelske, Christof
作者单位：University of London; University College London; Ruhr University Bochum
摘要：We consider-in a uniformly strictly convex potential regime-two versions of random gradient models with disorder. In model (A) the interface feels a bulk term of random fields while in model (B) the disorder enters through the potential acting on the gradients. We assume a general distribution on the disorder with uniformly-bounded finite second moments. It is well known that for gradient models without disorder there are no Gibbs measures in infinite volume in dimension , while there are shif...
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作者：Chernozhukov, Victor; Chetverikov, Denis; Kato, Kengo
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); University of California System; University of California Los Angeles; University of Tokyo
摘要：Slepian and Sudakov-Fernique type inequalities, which compare expectations of maxima of Gaussian random vectors under certain restrictions on the covariance matrices, play an important role in probability theory, especially in empirical process and extreme value theories. Here we give explicit comparisons of expectations of smooth functions and distribution functions of maxima of Gaussian random vectors without any restriction on the covariance matrices. We also establish an anti-concentration...
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作者：Erhard, D.; den Hollander, F.; Maillard, G.
作者单位：Leiden University; Leiden University - Excl LUMC; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Aix-Marseille Universite
摘要：We continue our study of the parabolic Anderson equation , where is the diffusion constant, is the discrete Laplacian, and plays the role of a dynamic random environment that drives the equation. The initial condition , is taken to be non-negative and bounded. The solution of the parabolic Anderson equation describes the evolution of a field of particles performing independent simple random walks with binary branching: particles jump at rate , split into two at rate , and die at rate . We assu...
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作者：Nguyen, Hoi H.; O'Rourke, Sean
作者单位：University System of Ohio; Ohio State University; Yale University
摘要：The circular law asserts that if is a matrix with iid complex entries of mean zero and unit variance, then the empirical spectral distribution of converges almost surely to the uniform distribution on the unit disk as tends to infinity. Answering a question of Tao, we prove the circular law for a general class of random block matrices with dependent entries. The proof relies on an inverse-type result for the concentration of linear operators and multilinear forms.
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作者：Krylov, N. V.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We prove that under Hormander's type conditions on the coefficients of the unobservable component of a partially observable diffusion process the filtering density is infinitely differentiable and can be represented as the integral of an infinitely differentiable kernel against the prior initial distribution. These results are derived from more general results obtained for SPDEs. One of the main novelties of the paper is the existence and smoothness of the kernel, another one is that we allow ...
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作者：Lu, Jianfeng; Nolen, James
作者单位：Duke University; Duke University
摘要：We study the trajectories of a solution to an It stochastic differential equation in , as the process passes between two disjoint open sets, and . These segments of the trajectory are called transition paths or reactive trajectories, and they are of interest in the study of chemical reactions and thermally activated processes. In that context, the sets and represent reactant and product states. Our main results describe the probability law of these transition paths in terms of a transition pat...
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作者：Arratia, Richard; Baxendale, Peter
作者单位：University of Southern California
摘要：Under the assumption that the distribution of a nonnegative random variable admits a bounded coupling with its size biased version, we prove simple and strong concentration bounds. In particular the upper tail probability is shown to decay at least as fast as the reciprocal of a Gamma function, guaranteeing a moment generating function that converges everywhere. The class of infinitely divisible distributions with finite mean, whose L,vy measure is supported on an interval contained in for som...
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作者：Bhatnagar, Nayantara; Peled, Ron
作者单位：University of Delaware; Tel Aviv University
摘要：We study the length of the longest increasing and longest decreasing subsequences of random permutations drawn from the Mallows measure. Under this measure, the probability of a permutation is proportional to where is a real parameter and is the number of inversions in . The case corresponds to uniformly random permutations. The Mallows measure was introduced by Mallows in connection with ranking problems in statistics. We determine the typical order of magnitude of the lengths of the longest ...
