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作者：Aimino, Romain; Nicol, Matthew; Vaienti, Sandro
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Physics (INP); Aix-Marseille Universite; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Physics (INP); Universite de Toulon; University of Houston System; University of Houston
摘要：In this paper, we investigate annealed and quenched limit theorems for random expanding dynamical systems. Making use of functional analytic techniques and more probabilistic arguments with martingales, we prove annealed versions of a central limit theorem, a large deviation principle, a local limit theorem, and an almost sure invariance principle. We also discuss the quenched central limit theorem, dynamical Borel-Cantelli lemmas, Erdos-R,nyi laws and concentration inequalities.
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作者：Le Gall, Jean-Francois
作者单位：Universite Paris Saclay
摘要：We study properties of the random metric space called the Brownian map. For every , we consider the connected components of the complement of the open ball of radius centered at the root, and we let be the number of those connected components that intersect the complement of the ball of radius . We then prove that converges as to a constant times the density at of the profile of distances from the root. In terms of the Brownian cactus, this gives asymptotics for the number of points at height ...
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作者：Damron, Michael; Hanson, Jack; Sosoe, Philippe
作者单位：Princeton University; Princeton University
摘要：We prove that the variance of the passage time from the origin to a point in first-passage percolation on is sublinear in the distance to when , obeying the bound , under minimal assumptions on the edge-weight distribution. The proof applies equally to absolutely continuous, discrete and singular continuous distributions and mixtures thereof, and requires only moments. The main result extends work of Benjamini-Kalai-Schramm (Ann Prob 31, 2003) and Benaim-Rossignol (Ann Inst Henri Poincar, Prob...
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作者：Li, Xinyi; Sznitman, Alain-Sol
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We derive a large deviation principle for the density profile of occupation times of random interlacements at a fixed level in a large box of , . As an application, we analyze the asymptotic behavior of the probability that atypically high values of the density profile insulate a macroscopic body in a large box. As a step in this program, we obtain a similar large deviation principle for the occupation-time measure of Brownian interlacements at a fixed level in a large box of , and we derive a...
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作者：Rakhlin, Alexander; Sridharan, Karthik; Tewari, Ambuj
作者单位：University of Pennsylvania; University of Michigan System; University of Michigan
摘要：We establish necessary and sufficient conditions for a uniform martingale Law of Large Numbers. We extend the technique of symmetrization to the case of dependent random variables and provide sequential (non-i.i.d.) analogues of various classical measures of complexity, such as covering numbers and combinatorial dimensions from empirical process theory. We establish relationships between these various sequential complexity measures and show that they provide a tight control on the uniform conv...
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作者：Cacciapuoti, Claudio; Maltsev, Anna; Schlein, Benjamin
作者单位：University of Bonn; University of Bristol
摘要：We consider ensembles of Wigner matrices, whose entries are (up to the symmetry constraints) independent and identically distributed random variables. We show the convergence of the Stieltjes transform towards the Stieltjes transform of the semicircle law on optimal scales and with the optimal rate. Our bounds improve previous results, in particular from ErdAs et al. (Adv Math 229(3):1435-1515, 2012; Electron J Probab 18(59):1-58, 2013), by removing the logarithmic corrections. As applications...
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作者：Calka, Pierre; Yukich, J. E.
作者单位：Universite de Rouen Normandie; Lehigh University
摘要：Let K-n be the convex hull of i.i.d. random variables distributed according to the standard normal distribution on . We establish variance asymptotics as for the re-scaled intrinsic volumes and -face functionals of , , resolving an open problem (Weil and Wieacker, Handbook of Convex Geometry, vol. B, pp. 1391-1438. North-Holland/Elsevier, Amsterdam, 1993). Variance asymptotics are given in terms of functionals of germ-grain models having parabolic grains with apices at a Poisson point process ...
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作者：Aizenman, Michael; Warzel, Simone
作者单位：Princeton University; Princeton University; Technical University of Munich
摘要：We consider the distribution of the values at real points of random functions which belong to the Herglotz-Pick (HP) class of analytic mappings of the upper half plane into itself. It is shown that under mild stationarity assumptions the individual values of HP functions with singular spectra have a Cauchy type distribution. The statement applies to the diagonal matrix elements of random operators, and holds regardless of the presence or not of level repulsion, i.e. applies to both random matr...
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作者：Mathieu, Pierre; Mourrat, Jean-Christophe
作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We show aging of Glauber-type dynamics on the random energy model, in the sense that we obtain the annealed scaling limits of the clock process and of the age process. The latter encodes the Gibbs weight of the configuration occupied by the dynamics. Both limits are expressed in terms of stable subordinators.
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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...
