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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...
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作者：Wang, Feng-Yu
作者单位：Beijing Normal University; Swansea University
摘要：Let P(t) be the diffusion semigroup generated by L := Delta + del V on a complete connected Riemannian manifold with Ric >= -(sigma(2)rho(2)(0) + c) for some constants sigma, c > 0 and rho(0) the Riemannian distance to a fixed point. It is shown that Pt is hypercontractive, or the log-Sobolev inequality holds for the associated Dirichlet form, provided - Hess(V) >= delta holds outside of a compact set for some constant delta > (1 +root 2)sigma root d-1. This indicates, at least in finite dimen...
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作者：Cox, J. Theodore; Schinazi, Rinaldo B.
作者单位：Syracuse University; University of Colorado System; University of Colorado at Colorado Springs
摘要：We study the ergodic theory of a multitype contact process with equal death rates and unequal birth rates on the d-dimensional integer lattice and OF regular trees. We prove that for birth rates in a certain interval there is coexistence on the tree, which by a result of Neuhauser is not possible on the lattice. We also prove a complete convergence result when the larger birth rate falls outside of this interval.
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作者：von Renesse, Max-K.; Sturm, Karl-Theodor
作者单位：Technical University of Berlin; University of Bonn
摘要：We construct a new random probability measure on the circle and on the unit interval which in both cases has a Gibbs structure with the relative entropy functional as Hamiltonian. It satisfies a quasi-invariance formula with respect to the action of smooth diffeomorphism of the sphere and the interval, respectively. The associated integration by parts formula is used to construct two classes of diffusion processes on probability measures (on the sphere or the unit interval) by Dirichlet form m...
