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作者：Imkeller, Peter; Pavlyukevich, Ilya; Wetzel, Torsten
作者单位：Humboldt University of Berlin
摘要：We consider a dynamical system described by the differential equation (Y) over dot(t) = -U'(Y-t) with a unique stable point at the origin. We perturb the system by the Levy noise of intensity E to obtain the stochastic differential equation dX(t)(epsilon) = -U'(X-t-(epsilon)) dt + epsilon dL(t). The process L is a symmetric Levy process whose jump measure nu has exponentially light tails, nu([u, infinity)) similar to exp(- u(alpha)), alpha > 0, u -> infinity. We study the first exit problem fo...
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作者：Melbourne, Ian; Nicol, Matthew
作者单位：University of Surrey; University of Houston System; University of Houston
摘要：We prove an almost sure invariance principle (approximation by d-dimensional Brownian motion) for vector-valued Holder observables of large classes of nonuniformly hyperbolic dynamical systems. These systems include Axiom A diffeomorphisms and flows as well as systems modeled by Young towers with moderate tail decay rates. In particular, the position variable of the planar periodic Lorentz gas with finite horizon approximates a two-dimensional Brownian motion.
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作者：Capitaine, Mireille; Donati-Martin, Catherine; Feral, Delphine
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Sorbonne Universite; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Inria; Universite de Bordeaux
摘要：In this paper, we investigate the asymptotic spectrum of complex or real Deformed Wigner matrices (M-N)(N) defined by M-N = W-N/root N + A(N) where W-N is all N x N Hermitian (resp., symmetric) Wigner matrix whose entries have a symmetric law satisfying a Poincare inequality. The matrix A(N) is Hermitian (resp., symmetric) and deterministic with all but finitely many eigenvalues equal to zero. We first show that, as soon as the first largest or last smallest eigenvalues of A(N) are sufficientl...
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作者：Gozlan, Nathael
作者单位：Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：The aim of this paper is to give a characterization of the dimension free concentration of measure phenomenon in terms of transportation-cost inequalities. We apply this theorem to give a new and very short proof of a result by Otto and Villani. Another application is to show that the Poincare inequality is equivalent to a certain form of dimension free exponential concentration. The proofs of all these results rely on simple Large Deviations techniques.
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作者：Erdos, Laszlo; Schlein, Benjamin; Yau, Horng-Tzer
作者单位：University of Munich; Harvard University
摘要：We consider N x N Hermitian random matrices with i.i.d. entries. The matrix is normalized so that the average spacing between consecutive eigenvalues is of order 1/N. We study the connection between eigenvalue statistics on microscopic energy scales eta << 1 and (de)localization properties of the eigenvectors. Under suitable assumptions on the distribution of the single matrix elements, we first give an upper bound on the density of states on short energy scales of order eta similar to log N/N...
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作者：Meerschaert, Mark M.; Nane, Erkan; Vellaisamy, P.
作者单位：Michigan State University; Auburn University System; Auburn University; Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Bombay
摘要：Fractional Cauchy problems replace the usual first-order time derivative by a fractional derivative. This paper develops classical solutions and stochastic analogues for fractional Cauchy problems in a bounded domain D subset of R-d with Dirichlet boundary conditions. Stochastic solutions are constructed via an inverse stable subordinator whose scaling index corresponds to the order of the fractional time derivative. Dirichlet problems corresponding to iterated Brownian motion in a bounded dom...
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作者：Bertini, Lorenzo; Landim, Claudio; Mourragui, Mustapha
作者单位：Sapienza University Rome; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider the weakly asymmetric exclusion process on a bounded interval with particle reservoirs at the endpoints. The hydrodynamic limit for the empirical density, obtained in the diffusive scaling, is given by the viscous Burgers equation with Dirichlet boundary conditions. We prove the associated dynamical large deviations principle.
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作者：Bobkov, Sergey G.; Ledoux, Michel
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：Brascamp-Lieb-type, weighted Poincare-type and related analytic inequalities are studied for multidimensional Cauchy distributions and more general kappa-concave probability measures (in the hierarchy of convex measures). In analogy with the limiting (infinite-dimensional log-concave) Gaussian model, the weighted inequalities fully describe the measure concentration and large deviation properties of this family of measures. Cheeger-type isoperimetric inequalities are investigated similarly, gi...
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作者：Krishnapur, Manjunath
作者单位：University of Toronto
摘要：We consider two families of random matrix-valued analytic functions: (1) G(1) - zG(2) and (2) G(0) + zG(1) + Z(2)G(2) + . . . , where G(i) are n x n random matrices with independent standard complex Gaussian entries. The random set of z where these matrix-analytic functions become singular is shown to be determinantal point processes in the sphere and the hyperbolic plane, respectively. The kernels of these determinantal processes are reproducing kernels of certain Hilbert spaces (Bargmann-Foc...
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作者：Pitman, Jim; Winkel, Matthias
作者单位：University of California System; University of California Berkeley; University of Oxford
摘要：We use a natural ordered extension of the Chinese Restaurant Process to grow a two-parameter family of binary self-similar continuum fragmentation trees. We provide an explicit embedding of Ford's sequence of alpha model trees in the continuum tree which we identified in a previous article as a distributional scaling limit of Ford's trees. In general, the Markov branching trees induced by the two-parameter growth rule are not sampling consistent, so the existence of compact limiting trees cann...
