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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...
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作者：Erde, J. O. S. H. U. A.; Kang, M. I. H. Y. U. N.; Krivelevich, M. I. C. H. A. E. L.
作者单位：Graz University of Technology; Tel Aviv University
摘要：It is well known that the behaviour of a random subgraph of a d-dimensional hypercube, where we include each edge independently with probability p, undergoes a phase transition when p is around 1/d More precisely, standard arguments show that just below this value of p all components of this graph have order O(d) with probability tending to one as d -> infinity (whp for short), whereas Ajtai, Komlos and Szemeredi (Combinatorica 2 (1982) 1-7) showed that just above this value, in the supercriti...
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作者：Alimohammadi, Yeganeh; Borgs, Christian; Saberi, Amin
作者单位：Stanford University; University of California System; University of California Berkeley
摘要：We study random digraphs on sequences of expanders with a bounded average degree which converge locally in probability. We prove that the rel-ative size and the threshold for the existence of a giant strongly connected component as well as the asymptotic fraction of nodes with giant fan-in or nodes with giant fan-out are local, in the sense that they are the same for two sequences with the same local limit. The digraph has a bow-tie structure, with all but a vanishing fraction of nodes lying e...
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作者：Alishahi, Kasra; Barzegar, Milad; Zamani, Mohammadsadegh
作者单位：Sharif University of Technology; University of Yazd
摘要：We prove that every negatively associated sequence of Bernoulli random variables with summable covariances has a trivial tail a-field. A corollary of this result is the tail triviality of strongly Rayleigh processes. This is a gen-eralization of a result due to Lyons, which establishes tail triviality for dis-crete determinantal processes. We also study the tail behavior of negatively associated Gaussian and Gaussian threshold processes. We show that these processes are tail trivial though, in...
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作者：Dumaz, Laure; Labbe, Cyril
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Universite Paris Cite
摘要：We introduce a random differential operator that we call CS tau operator, whose spectrum is given by the Sch(tau) point process introduced by Kritchevski, Valko and Virag (Comm. Math Phys. (2012) 314 775-806) and whose eigen-vectors match with the description provided by Rifkind and Virag (Geom. Funct. Anal. (2018) 28 1394-1419). This operator acts on R-2-valued func-tions from the interval [0, 1] and takes the form [GRAPHICS] . where dB, dW(1) and dW(2) are independent white noises. Then we i...
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作者：Chen, Xin; LI, Xue-mei; Wu, Bo
作者单位：Shanghai Jiao Tong University; Imperial College London; Fudan University
摘要：The main results of the article are short time estimates and asymptotic estimates for the first two order derivatives of the logarithmic heat kernel of a complete Riemannian manifold. We remove all curvature restrictions and also develop several techniques.A basic tool developed here is intrinsic stochastic variations with pre-scribed second order covariant differentials, allowing to obtain a path inte-gration representation for the second order derivatives of the heat semigroup Pt on a comple...
