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作者：Bhamidi, Shankar; Sen, Sanchayan
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Indian Institute of Science (IISC) - Bangalore
摘要：A well-known open problem on the behavior of optimal paths in random graphs in the strong disorder regime, formulated by statistical physicists, and supported by a large amount of numerical evidence over the last decade (Braunstein et al. in Phys RevLett 91(16):168701, 2003; Braunstein et al. in Int J Bifurc Chaos 17(07):2215-2255,2007; Chen et al. in Phys Rev Lett 96(6):068702, 2006; Wu et al. in Phys Rev Lett96(14):148702, 2006) is as follows: for a large class of random graph models with de...
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作者：Carlier, Guillaume; Delalande, Alex; Merigot, Quentin
作者单位：Universite PSL; Universite Paris-Dauphine; Inria; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Institut Universitaire de France
摘要：Wasserstein barycenters define averages of probability measures in a geometrically meaningful way. Their use is increasingly popular in applied fields, such as image, geometry or language processing. In these fields however, the probability measures of interest are often not accessible in their entirety and the practitioner may have to deal with statistical or computational approximations instead. In this article, we quantify the effect of such approximations on the corresponding barycenters. ...
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作者：Hairer, Martin; Le, Khoa; Rosati, Tommaso
作者单位：Imperial College London; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Technical University of Berlin; University of Leeds; University of Warwick
摘要：We consider the Allen-Cahn equation ?(t)u - ?u = u - u(3) with a rapidly mixing Gaussian field as initial condition. We show that provided that the amplitude of the initial condition is not too large, the equation generates fronts described by nodal sets of the Bargmann-Fock Gaussian field, which then evolve according to mean curvature flow.
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作者：Penrose, Mathew D.
作者单位：University of Bath
摘要：Let X-1, X-2, . . . be independent random uniform points in a bounded domain A subset of R-d with smooth boundary. Define the coverage threshold Rn to be the smallest r such that A is covered by the balls of radius r centred on X-1, . . . , X-n. We obtain the limiting distribution of R(n )and also a strong law of large numbers for R-n in the large -n limit. For example, if A has volume 1 and perimeter |& part; A|, if d = 3 then P[n pi R-n(3) - log n - 2 log(log n) <= x] converges to exp(-2(-4)...
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作者：Matetski, Konstantin; Remenik, Daniel
作者单位：Columbia University; Universidad de Chile; Universidad de Chile
摘要：The explicit biorthogonalization method, developed in [24] for continuous time TASEP, is generalized to a broad class of determinantal measures which describe the evolution of several interacting particle systems in the KPZ universality class. The method is applied to sequential and parallel update versions of each of the four variants of discrete time TASEP (with Bernoulli and geometric jumps, and with block and push dynamics) which have determinantal transition probabilities; to continuous t...
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作者：Yu, Lei
作者单位：Nankai University; Nankai University
摘要：Given a convex function 0 : [0, 1] ? R and the mean ? f (X) = a ? [0, 1], which Boolean function f maximizes the 0-stability E[F (T-? f(X))] of f ? Here X is a random vector uniformly distributed on the discrete cube {-1, 1}n and T(? )is the Bonami-Beckner operator. Special cases of this problem include the (symmetric and asymmetric) a-stability problems and the Most Informative Boolean Function problem. In this paper, we provide several upper bounds for the maximal 0-stability. When specializ...
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作者：Ahn, Andrew
作者单位：Cornell University
摘要：We establish universality for the largest singular values of products of random matrices with right unitarily invariant distributions, in a regime where the number of matrix factors and size of thematrices tend to infinity simultaneously. The behavior of the largest log singular values coincides with the large N limit of Dyson Brownian motion with a characteristic drift vector consisting of equally spaced coordinates, which matches the large N limit of the largest log singular values of Browni...
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作者：Hong, Wei; Li, Shihu; Liu, Wei; Sun, Xiaobin
作者单位：Jiangsu Normal University; Tianjin University
摘要：Themain aim of thiswork is to study the asymptotic behavior formulti-scaleMcKeanVlasov stochastic dynamical systems. Firstly, we obtain a central limit type theorem, i.e. the deviation between the slow component X-epsilon and the solution X- of the averaged equation converges weakly to a limiting process. More precisely, X epsilon-X-|root epsilon v e converges weakly in C([0, T], R-n) to the solution of certain distribution dependent stochastic differential equation, which involves an extra ex...
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作者：Subag, Eliran
作者单位：Weizmann Institute of Science
摘要：We compute the free energy at all temperatures for the spherical pure p-spin models from the generalized Thouless-Anderson-Palmer representation. This is the first example of a mixed p-spin model for which the free energy is computed in the whole replica symmetry breaking phase, without appealing to the famous Parisi formula.
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作者：Mao, Cheng; Rudelson, Mark; Tikhomirov, Konstantin
作者单位：University System of Georgia; Georgia Institute of Technology; University of Michigan System; University of Michigan
摘要：This paper deals with the problem of graph matching or network alignment for Erdos- Renyi graphs, which can be viewed as a noisy average-case version of the graph isomorphism problem. Let G and G' be G(n, p) Erdos-Renyi graphs marginally, identified with their adjacency matrices. Assume that G and G' are correlated such that E[G(ij)G'(ij)] = p(1 - alpha). For a permutation pi representing a latent matching between the vertices of G and G', denote by G(pi) the graph obtained from permuting the ...
