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作者：Holcomb, Diane; Valko, Benedek
作者单位：University of Arizona; University of Wisconsin System; University of Wisconsin Madison
摘要：The process is the bulk point process limit of the Gaussian -ensemble. For and 4 this process gives the limit of the GOE, GUE and GSE random matrix models. The process is obtained similarly as the bulk scaling limit of the spectrum of certain discrete one-dimensional random Schrodinger operators. Both point processes have asymptotically constant average density, in our chosen normalization one expects close to points in a large interval of length . We prove large deviation principles for the a...
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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...
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作者：Beltran, J.; Landim, C.
作者单位：Pontificia Universidad Catolica del Peru; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rouen Normandie
摘要：We presented in Beltran and Landim ( J Stat Phys 140:1065-1114, 2010) Beltran and Landim (J Stat Phys 149:598-618, 2012) an approach to derive the metastable behavior of continuous-time Markov chains. We assumed in these articles that the Markov chains visit points in the time scale in which it jumps among the metastable sets. We replace this condition here by assumptions on the mixing times and on the relaxation times of the chains reflected at the boundary of the metastable sets.
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作者：Mischler, Stephane; Mouhot, Clement; Wennberg, Bernt
作者单位：Universite PSL; Universite Paris-Dauphine; University of Cambridge; Chalmers University of Technology; University of Gothenburg
摘要：This paper is devoted the study of the mean field limit for many-particle systems undergoing jump, drift or diffusion processes, as well as combinations of them. The main results are quantitative estimates on the decay of fluctuations around the deterministic limit and of correlations between particles, as the number of particles goes to infinity. To this end we introduce a general functional framework which reduces this question to the one of proving a purely functional estimate on some abstr...
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作者：Bordenave, Charles; Caputo, Pietro
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National des Sciences Appliquees de Toulouse; Roma Tre University
摘要：Consider the ErdAs-Renyi random graph on vertices where each edge is present independently with probability , with fixed. For large , a typical random graph locally behaves like a Galton-Watson tree with Poisson offspring distribution with mean . Here, we study large deviations from this typical behavior within the framework of the local weak convergence of finite graph sequences. The associated rate function is expressed in terms of an entropy functional on unimodular measures and takes finit...
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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...
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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 ...
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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...
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作者：De Masi, Anna; Ferrari, Pablo A.; Presutti, Errico
作者单位：University of L'Aquila; University of Buenos Aires; Universidade de Sao Paulo; Gran Sasso Science Institute (GSSI)
摘要：We consider the one dimensional symmetric simple exclusion process with additional births and deaths restricted to a subset of configurations where there is a leftmost hole and a rightmost particle. At a fixed rate birth of particles occur at the position of the leftmost hole and at the same rate, independently, the rightmost particle dies. We prove convergence to a hydrodynamic limit and discuss its relation with a free boundary problem.
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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...
