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作者：Gozlan, Nathael; Roberto, Cyril; Samson, Paul-Marie
作者单位：Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：We show that Talaurand's transport inequality is equivalent to a restricted logarithmic Sobolev inequality. This result clarifies the links between these two important functional inequalities. As an application, we give the first proof of the fact that Talagrand's inequality is stable under bounded perturbations.
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作者：Mendelson, Shahar
作者单位：Technion Israel Institute of Technology; Australian National University
摘要：We show that for a typical coordinate projection of a subgaussian class of functions, the infimum over signs inf((epsilon i)) sup f epsilon F |Sigma(k)(i)=1 epsilon(i) f (X-i)| is asymptotically smaller than the expectation over signs as a function of the dimension k, if the canonical Gaussian process indexed by F is continuous. To that end, we establish a bound on the discrepancy of an arbitrary subset of R-k using properties of the canonical Gaussian process the set indexes, and then obtain ...
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作者：Saloff-Coste, L.; Zuniga, J.
作者单位：Cornell University; Stanford University
摘要：We study time-inhomogeneous Markov chains with finite state spaces using Nash and logarithmic-Sobolev inequalities, and the notion of c-stability. We develop the basic theory of such functional inequalities in the time-inhomogeneous context and provide illustrating examples.
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作者：Gloria, Antoine; Otto, Felix
作者单位：Max Planck Society
摘要：We consider a discrete elliptic equation on the d-dimensional lattice Z(d) with random coefficients A of the simplest type: they are identically distributed and independent from edge to edge. On scales large w.r.t. the lattice spacing (i.e., unity), the solution operator is known to behave like the solution operator of a (continuous) elliptic equation with constant deterministic coefficients. This symmetric homogenized matrix A(hom) = a(hom) Id is characterized by xi . A(hom)xi = <(xi + del ph...
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作者：Benjamini, Itai; Gurel-Gurevich, Ori; Schramm, Oded
作者单位：Weizmann Institute of Science; Microsoft
摘要：We construct a bounded degree graph G, such that a simple random walk on it is transient but the random walk path (i.e., the subgraph of all the edges the random walk has crossed) has only finitely many cutpoints, almost surely. We also prove that the expected number of cutpoints of any transient Markov chain is infinite. This answers two questions of James, Lyons and Peres [A Transient Markov Chain With Finitely Many Cutpoints (2007) Festschrift for David Freedman]. Additionally, we consider ...
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作者：Pardon, John
作者单位：Princeton University
摘要：We study the probability distribution of the area and the number of vertices of random polygons in a convex set K subset of R-2. The novel aspect of our approach is that it yields uniform estimates for all convex sets K subset of R-2 without imposing any regularity conditions on the boundary partial derivative K. Our main result is a central limit theorem for both the area and the number of vertices, setting a well-known conjecture in the field. We also obtain asymptotic results relating the g...
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作者：Benaych-Georges, Florent; Levy, Thierry
作者单位：Universite Paris Cite; Sorbonne Universite; Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
摘要：In this paper, we investigate a continuous family of notions of independence which interpolates between the classical and free ones for noncommutative random variables. These notions are related to the liberation process introduced by Voiculescu. To each notion of independence correspond new convolutions of probability measures, for which we establish formulae and of which we compute simple examples. We prove that there exists no reasonable analogue of classical and free cumulants associated t...
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作者：Bordenave, Charles; Lelarge, Marc; Salez, Justin
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National des Sciences Appliquees de Toulouse; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We investigate the rank of the adjacency matrix of large diluted random graphs: for a sequence of graphs (G(n))(n >= 0) converging locally to a Galton-Watson tree T (GWT), we provide an explicit formula for the asymptotic multiplicity of the eigenvalue 0 in terms of the degree generating function phi(*) of T. In the first part, we show that the adjacency operator associated with T is always self-adjoint; we analyze the associated spectral measure at the root and characterize the distribution o...
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作者：Kurtz, Thomas G.; Rodrigues, Eliane R.
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison; Universidad Nacional Autonoma de Mexico
摘要：Representations of branching Markov processes and their measure-valued limits in terms of countable systems of particles are constructed for models with spatially varying birth and death rates. Each particle has a location and a level, but unlike earlier constructions, the levels change with time. In fact, death of a particle occurs only when the level of the particle crosses a specified level r, or for the limiting models, hits infinity. For branching Markov processes, at each time t conditio...
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作者：Kuznetsov, Alexey
作者单位：York University - Canada
摘要：We study the Wiener-Hopf factorization and the distribution of extrema for general stable processes. By connecting the Wiener-Hopf factors with a certain elliptic-like function we are able to obtain many explicit and general results, such as infinite series representations and asymptotic expansions for the density of supremum, explicit expressions for the Wiener-Hopf factors and the Mellin transform of the supremum, quasi-periodicity and functional identities for these functions, finite produc...
