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作者：Aggarwal, Amol
摘要：In this paper we consider NxN real generalized Wigner matrices whose entries are only assumed to have finite (2+epsilon)th moment for some fixed, but arbitrarily small, epsilon>0. We show that the Stieltjes transforms mN(z) of these matrices satisfy a weak local semicircle law on the nearly smallest possible scale, when =I(z) is almost of order N-1. As a consequence, we establish bulk universality for local spectral statistics of these matrices at fixed energy levels, both in terms of eigenval...
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作者：Lugosi, Gabor; Mendelson, Shahar
作者单位：Pompeu Fabra University; ICREA; Universite Paris Cite; Sorbonne Universite; Australian National University
摘要：We study the problem of estimating the mean of a random vector in based on an i.i.d. sample, when the accuracy of the estimator is measured by a general norm on . We construct an estimator (that depends on the norm) that achieves an essentially optimal accuracy/confidence tradeoff under the only assumption that the random vector has a well-defined covariance matrix. At the heart of the argument is the construction of a uniform median-of-means estimator in a class of real valued functions.
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作者：Kopfer, Eva
作者单位：University of Bonn
摘要：We introduce Brownian motions on time-dependent metric measure spaces, proving their existence and uniqueness. We prove contraction estimates for their trajectories assuming that the time-dependent heat flow satisfies transport estimates with respect to every L-p-Kantorovich distance, p. [1,8]. These transport estimates turn out to characterize super-Ricci flows, introduced by Sturm (J Funct Anal 275(12):3504-3569, 2015.)
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作者：Hutchcroft, Tom; Peres, Yuval
作者单位：University of Cambridge; Microsoft
摘要：We prove that the uniform spanning forests of Z(d) and Z(l) have qualitatively different connectivity properties whenever l > d >= 4. In particular, we consider the graph formed by contracting each tree of the uniform spanning forest down to a single vertex, which we call the component graph. We introduce the notion of ubiquitous subgraphs and show that the set of ubiquitous subgraphs of the component graph changes whenever the dimension changes and is above 8. To separate dimensions 5, 6, 7, ...
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作者：Erschler, Anna
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
摘要：We study the neighborhoods of a typical point Zn visited at n-th step of a random walk, determined by the condition that the transition probabilities stay close to n(Zn). If such neighborhood contains a ball of radius Cn, we say that the random walk has almost invariant transition probabilities. We prove that simple random walks on wreath products of Z with finite groups have almost invariant distributions. A weaker version of almost invariance implies a necessary condition of Ozawa's criterio...
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作者：Chatterjee, Sourav
作者单位：Stanford University
摘要：A random set of points in Euclidean space is called 'rigid' or 'hyperuniform' if the number of points falling inside any given region has significantly smaller fluctuations than the corresponding number for a set of i.i.d. random points. This phenomenon has received considerable attention in recent years, due to its appearance in random matrix theory, the theory of Coulomb gases and zeros of random analytic functions. However, most of the published results are in dimensions one and two. This p...
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作者：Barbier, Jean; Macris, Nicolas
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Abdus Salam International Centre for Theoretical Physics (ICTP)
摘要：In recent years important progress has been achieved towards proving the validity of the replica predictions for the (asymptotic) mutual information (or free energy) in Bayesian inference problems. The proof techniques that have emerged appear to be quite general, despite they have been worked out on a case-by-case basis. Unfortunately, a common point between all these schemes is their relatively high level of technicality. We present a new proof scheme that is quite straightforward with respe...
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作者：Breit, Dominic; Feireisl, Eduard; Hofmanova, Martina; Maslowski, Bohdan
作者单位：Heriot Watt University; Czech Academy of Sciences; Institute of Mathematics of the Czech Academy of Sciences; Technical University of Berlin; Charles University Prague
摘要：We study the long-time behavior of solutions to a stochastically driven Navier-Stokes system describing the motion of a compressible viscous fluid driven by a temporal multiplicative white noise perturbation. The existence of stationary solutions is established in the framework of Lebesgue-Sobolev spaces pertinent to the class of weak martingale solutions. The methods are based on new global-in-time estimates and a combination of deterministic and stochastic compactness arguments. An essential...
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作者：Boutillier, Cedric; de Tiliere, Beatrice; Raschel, Kilian
作者单位：Universite Paris Cite; Sorbonne Universite; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); Universite de Tours
摘要：The Z-invariant Ising model(Baxter in Philos Trans R Soc Lond A Math Phys Eng Sci 289(1359):315-346, 1978) is defined on an isoradial graph and has coupling constants depending on an elliptic parameter k. When k=0 the model is critical, and as k varies the whole range of temperatures is covered. In this paper we study the corresponding dimer model on the Fisher graph, thus extending our papers(Boutillier and de Tiliere in Probab Theory Relat Fields 147:379-413, 2010; Commun Math Phys 301(2):47...
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作者：Berger, Quentin; Giacomin, Giambattista; Lacoin, Hubert
作者单位：Sorbonne Universite; Universite Paris Cite; Universite Paris Cite; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：The copolymer model is a disordered system built on a discrete renewal process with inter-arrival distribution that decays in a regularly varying fashion with exponent 1+alpha >= 1. It exhibits a localization transition which can be characterized in terms of the free energy of the model: the free energy is zero in the delocalized phase and it is positive in the localized phase. This transition, which is observed when tuning the mean h of the disorder variable, has been tackled in the physics l...
