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作者：Muirhead, Stephen; Rivera, Alejandro; Vanneuville, Hugo; Kohler-Schindler, Laurin
作者单位：University of London; Queen Mary University London; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We develop techniques to study the phase transition for planar Gaussian percolation models that are not (necessarily) positively correlated. These models lack the property of positive associations (also known as the 'FKG inequality'), and hence many classical arguments in percolation theory do not apply. More precisely, we consider a smooth stationary centred planar Gaussian field f and, given a level l epsilon R, we study the connectivity properties of the excursion set {f >= -l}. We prove th...
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作者：Blumenthal, Alex; Zelati, Michele Coti; Gvalani, Rishabh S.
作者单位：University System of Georgia; Georgia Institute of Technology; Imperial College London; Max Planck Society
摘要：We consider the question of exponential mixing for random dynamical systems on arbitrary compact manifolds without boundary. We put forward a robust, dynamics-based framework that allows us to construct space-time smooth, uniformly bounded in time, universal exponential mixers. The framework is then applied to the problem of proving exponential mixing in a classical example proposed by Pierrehumbert in 1994, consisting of alternating periodic shear flows with randomized phases. This settles a ...
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作者：Subag, Eliran
作者单位：Weizmann Institute of Science
摘要：In a companion paper we developed the generalized TAP approach for general multispecies spherical mixed p-spin models. In this paper we use it to compute the limit of the free energy at any temperature for all pure mul-tispecies spherical p-spin models, assuming that certain free energies con-verge. Importantly, the pure multispecies models do not satisfy the convexity assumption on the mixture which was crucial in the recent proofs of the Parisi formula for the multispecies Sherrington-Kirkpa...
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作者：Hofmanova, Martina; Zhu, Rongchan; Zhu, Xiangchan
作者单位：University of Bielefeld; Beijing Institute of Technology; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：We are concerned with the three-dimensional incompressible Navier- Stokes equations driven by an additive stochastic forcing of trace class. First, for every divergence free initial condition in L2 we establish existence of infinitely many global-in-time probabilistically strong and analytically weak solutions, solving one of the open problems in the field. This result, in partic-ular, implies nonuniqueness in law. Second, we prove nonuniqueness of the associated Markov processes in a suitably...
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作者：Kozma, Gady; Samotij, Wojciech
作者单位：Weizmann Institute of Science; Tel Aviv University
摘要：We show that the naive mean-field approximation correctly predicts the leading term of the logarithmic lower tail probabilities for the number of copies of a given subgraph in G(n, p) and of arithmetic progressions of a given length in random subsets of the integers in the entire range of densities where the mean-field approximation is viable.Our main technical result provides sufficient conditions on the maximum degrees of a uniform hypergraph ?-L that guarantee that the logarithmic lower tai...
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作者：Thoma, Eric
作者单位：New York University
摘要：We characterize the behavior of a random discrete interface phi on [-L, L](d) boolean AND Z(d) with energy Sigma V (Delta phi(x)) as L -> infinity, where Delta is the discrete Laplacian and V is a uniformly convex, symmetric, and smooth potential. The interface phi is called the non-Gaussian membrane model. By analyzing the Helffer-Sjostrand representation, associated to Delta phi, we provide a unified approach to continuous scaling limits of the rescaled and interpolated inter-face in dimensi...
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作者：Benjamini, Itai; Tov, Hagai Helman; Zhukovskii, Maksim
作者单位：Weizmann Institute of Science
摘要：We observe the outcome of the discrete time noisy voter model at a single vertex of a graph. We show that certain pairs of graphs can be distinguished by the frequency of repetitions in the sequence of observations. We prove that this statistic is asymptotically normal and that it distinguishes between (asymptotically) almost all pairs of finite graphs. We conjecture that the noisy voter model distinguishes between any two graphs other than stars.
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作者：Bertini, Lorenzo; Gabrielli, Davide; Landim, Claudio
作者单位：Sapienza University Rome; University of L'Aquila
摘要：We consider the weakly asymmetric exclusion process on the d-dimensional torus. We prove a large deviations principle for the time averaged empirical density and current in the joint limit in which both the time interval and the number of particles diverge. This result is obtained both by analyzing the variational convergence, as the number of particles diverges, of the Donsker-Varadhan functional for the empirical process and by considering the large time behavior of the hydrodynamical rate f...
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作者：Cipolloni, Giorgio; Erdos, Laszlo; Schroeder, Dominik; Xu, Yuanyuan
作者单位：Princeton University; Institute of Science & Technology - Austria; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We establish a precise three-term asymptotic expansion, with an optimal estimate of the error term, for the rightmost eigenvalue of an n x n random matrix with independent identically distributed complex entries as n tends to infinity. All terms in the expansion are universal.
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作者：Biswas, Ratul; Chen, Wei-kuo; Sen, Arnab
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We study a diluted mean-field spin glass model with a quadratic Hamil-tonian. Our main result establishes the limiting free energy in terms of an in-tegral of a family of random variables that are the weak limits of the quenched variances of the spins in the system with varying edge connectivity. The key ingredient in our argument is played by the identification of these random variables as the unique solution to a recursive distributional equation. Our re-sults in particular provide the first...
