3-4期

最新文章

• Noncommutative martingale deviation and Poincar, type inequalities with applications AI翻译
  作者：Junge, Marius; Zeng, Qiang
  作者单位：University of Illinois System; University of Illinois Urbana-Champaign
  摘要：We prove a deviation inequality for noncommutative martingales by extending Oliveira's argument for random matrices. By integration we obtain a Burkholder type inequality with satisfactory constant. Using continuous time, we establish noncommutative Poincar, type inequalities for nice semigroups with a positive curvature condition. These results allow us to prove a general deviation inequality and a noncommutative transportation inequality due to Bobkov and Gotze in the commutative case. To de...
• How quickly can we sample a uniform domino tiling of the square via Glauber dynamics? AI翻译
  作者：Laslier, Benoit; Toninelli, Fabio Lucio
  作者单位：Universite Claude Bernard Lyon 1; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
  摘要：The prototypical problem we study here is the following. Given a square, there are approximately ways to tile it with dominos, i.e. with horizontal or vertical rectangles, where is Catalan's constant (Kasteleyn in Physica 27:1209-1225, 1961; Temperley and Fisher in Phil Mag 6:1061-1063, 1997). A conceptually simple (even if computationally not the most efficient) way of sampling uniformly one among so many tilings is to introduce a Markov Chain algorithm (Glauber dynamics) where, with rate , t...
• The topology of probability distributions on manifolds AI翻译
  作者：Bobrowski, Omer; Mukherjee, Sayan
  作者单位：Duke University; Duke University; Duke University; Duke University
  摘要：Let be a set of random points in , generated from a probability measure on a -dimensional manifold . In this paper we study the homology of -the union of -dimensional balls of radius around , as , and . In addition we study the critical points of -the distance function from the set . These two objects are known to be related via Morse theory. We present limit theorems for the Betti numbers of , as well as for number of critical points of index for . Depending on how fast decays to zero as grow...
• 1D log gases and the renormalized energy: crystallization at vanishing temperature AI翻译
  作者：Sandier, Etienne; Serfaty, Sylvia
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Institut Universitaire de France; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); New York University
  摘要：We study the statistical mechanics of a one-dimensional log gas or -ensemble with general potential and arbitrary , the inverse of temperature, according to the method we introduced for two-dimensional Coulomb gases in Sandier and Serfaty (Ann Probab, 2014). Such ensembles correspond to random matrix models in some particular cases. The formal limit corresponds to weighted Fekete sets and is also treated. We introduce a one-dimensional version of the renormalized energy of Sandier and Serfaty ...
• On properties of Parisi measures AI翻译
  作者：Auffinger, Antonio; Chen, Wei-Kuo
  作者单位：University of Chicago
  摘要：We investigate the structure of Parisi measures, the functional order parameters of mixed -spin models in mean field spin glasses. In the absence of external field, we prove that a Parisi measure satisfies the following properties. First, at all temperatures, the support of any Parisi measure contains the origin. If it contains an open interval, then the measure has a smooth density on this interval. Next, we give a criterion on temperature parameters for which a Parisi measure is neither Repl...
• Persistence of integrated stable processes AI翻译
  作者：Profeta, Christophe; Simon, Thomas
  作者单位：Universite Paris Saclay; Universite de Lille; Universite Paris Saclay
  摘要：We compute the persistence exponent of the integral of a stable L,vy process in terms of its self-similarity and positivity parameters. This solves a problem raised by Shi (Lower tails of some integrated processes. In: Small deviations and related topics (problem panel 2003). Along the way, we investigate the law of the stable process evaluated at the first time its integral hits zero, when the bivariate process starts from a coordinate axis. This extends classical formul' by McKean (J Math Ky...
• On the rate of convergence in Wasserstein distance of the empirical measure AI翻译
  作者：Fournier, Nicolas; Guillin, Arnaud
  作者单位：Sorbonne Universite; Universite Clermont Auvergne (UCA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
  摘要：Let be the empirical measure associated to a -sample of a given probability distribution on . We are interested in the rate of convergence of to , when measured in the Wasserstein distance of order . We provide some satisfying non-asymptotic -bounds and concentration inequalities, for any values of and . We extend also the non asymptotic -bounds to stationary -mixing sequences, Markov chains, and to some interacting particle systems.
• On the probability of staying above a wall for the -dimensional SOS model at low temperature AI翻译
  作者：Caputo, Pietro; Martinelli, Fabio; Toninelli, Fabio Lucio
  作者单位：Roma Tre University; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
  摘要：We obtain sharp asymptotics for the probability that the -dimensional discrete SOS interface at low temperature is positive in a large region. For a square region , both under the infinite volume measure and under the measure with zero boundary conditions around , this probability turns out to behave like , with the surface tension at zero tilt, also called step free energy, and L the box side. This behavior is qualitatively different from the one found for continuous height massless gradient ...
• Determinantal processes and completeness of random exponentials: the critical case AI翻译
  作者：Ghosh, Subhroshekhar
  作者单位：Princeton University
  摘要：For a locally finite point set , consider the collection of exponential functions given by . We examine the question whether spans the Hilbert space , when is random. For several point processes of interest, this belongs to a certain critical case of the corresponding question for deterministic , about which little is known. For the continuum sine kernel process, obtained as the bulk limit of GUE eigenvalues, we establish that is indeed complete almost surely. We also answer an analogous quest...
• KPZ relation does not hold for the level lines and flow lines of the Gaussian free field AI翻译
  作者：Aru, Juhan
  作者单位：Ecole Normale Superieure de Lyon (ENS de LYON)
  摘要：In this paper we mingle the Gaussian free field, the Schramm-Loewner evolution (SLE) and the KPZ relation in a natural way, shedding new light on all of them. In particular, we describe the quantum fractal behaviour of the level lines and the flow lines of the Gaussian free field by determining their quantum Minkowski dimensions. As a corollary we deduce that the usual KPZ relation is not satisfied. In order to determine the fractal dimensions, we have to make a technical detour: by a careful ...