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作者：Diaz, Mario; Mingo, James A.; Belinschi, Serban T.
作者单位：Queens University - Canada; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：In this paper we study the global fluctuations of block Gaussian matrices within the framework of second-order free probability theory. In order to compute the second-order Cauchy transform of these matrices, we introduce a matricial second-order conditional expectation and compute the matricial second-order Cauchy transform of a certain type of non-commutative random variables. As a by-product, using the linearization technique, we obtain the second-order Cauchy transform of non-commutative r...
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作者：Hutchcroft, Tom
作者单位：University of Cambridge
摘要：We prove that the wired uniform spanning forest exhibits mean-field behaviour on a very large class of graphs, including every transitive graph of at least quintic volume growth and every bounded degree nonamenable graph. Several of our results are new even in the case of Z(d), d >= 5. In particular, we prove that every tree in the forest has spectral dimension 4/3 and walk dimension 3 almost surely, and that the critical exponents governing the intrinsic diameter and volume of the past of a v...
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作者：van der Hofstad, Remco; Hulshof, Tim; Nagel, Jan
作者单位：Eindhoven University of Technology; Dortmund University of Technology
摘要：Let T be a supercritical Galton-Watson tree with a bounded offspring distribution that has mean mu > 1, conditioned to survive. Let phi T be a random embedding of T into Z(d) according to a simple random walk step distribution. Let T-p be percolation on T with parameter p, and let p(c) = mu(-1) be the critical percolation parameter. We consider a random walk (X-n)(n >= 1) on T-p and investigate the behavior of the embedded process phi T-p (X-n) as n -> infinity and simultaneously, T-p becomes ...
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作者：Tsatsoulis, Pavlos; Weber, Hendrik
作者单位：Max Planck Society; University of Bath
摘要：We prove an asymptotic coupling theorem for the 2-dimensional Allen-Cahn equation perturbed by a small space-time white noise. We show that with overwhelming probability two profiles that start close to the minimisers of the potential of the deterministic system contract exponentially fast in a suitable topology. In the 1-dimensional case a similar result was shown in Martinelli et al. (Commun Math Phys 120(1):25-69, 1988; J Stat Phys 55(3-4):477-504, 1989). It is well-known that in two or mor...
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作者：Dubedat, Julien; Falconet, Hugo
作者单位：Columbia University
摘要：We study the Liouville metric associated to an approximation of a log-correlated Gaussian field with short range correlation. We show that below a parameter gamma(c) > 0, the left-right length of rectangles for the Riemannian metric e(gamma phi 0,n)ds(2) with various aspect ratio is concentrated with quasi-lognormal tails, that the renormalized metric is tight when gamma < min(gamma(c), 0.4) and that subsequential limits are consistent with the Weyl scaling.
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作者：Holden, Nina; Sheffield, Scott
作者单位：Massachusetts Institute of Technology (MIT)
摘要：The Schelling model of segregation, introduced by Schelling in 1969 as a model for residential segregation in cities, describes how populations of multiple types self-organize to form homogeneous clusters of one type. In this model, vertices in an N-dimensional lattice are initially assigned types randomly. As time evolves, the type at a vertex v has a tendency to be replaced with the most common type within distance w of v. We present the first mathematical description of the dynamical scalin...
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作者：Zhang, Deng
作者单位：Shanghai Jiao Tong University
摘要：We study optimal control problems for stochastic nonlinear Schrodinger equations in both the mass subcritical and critical case. For general initial data of the minimal L-2 regularity, we prove the existence and first order Lagrange condition of an open loop control. In particular, these results apply to the stochastic nonlinear Schrodinger equations with the critical quintic and cubic nonlinearities in dimensions one and two, respectively. Furthermore, we obtain uniform estimates of (backward...
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作者：Burdzy, Krzysztof; Pal, Soumik
作者单位：University of Washington; University of Washington Seattle
摘要：We consider random labelings of finite graphs conditioned on a small fixed number of peaks. We introduce a continuum framework where a combinatorial graph is associated with a metric graph and edges are identified with intervals. Next we consider a sequence of partitions of the edges of the metric graph with the partition size going to zero. As the mesh of the subdivision goes to zero, the conditioned random labelings converge, in a suitable sense, to a deterministic function which evolves as ...
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作者：Gigli, Nicola; Tamanini, Luca
作者单位：International School for Advanced Studies (SISSA); University of Bonn
摘要：In this paper we prove that, within the framework of RCD* (K, N) spaces with N < infinity, the entropic cost (i.e. the minimal value of the Schrodinger problem) admits: A threefold dynamical variational representation, in the spirit of the Benamou-Brenier formula for the Wasserstein distance; A Hamilton-Jacobi-Bellman dual representation, in line with Bobkov-Gentil-Ledoux and Otto-Villani results on the duality between Hamilton-Jacobi and continuity equation for optimal transport; A Kantorovic...
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作者：Hutchcroft, Tom
作者单位：University of Cambridge
摘要：Let G be a Cayley graph of a nonamenable group with spectral radius rho<1. It is known that branching random walk on G with offspring distribution mu is transient, i.e., visits the origin at most finitely often almost surely, if and only if the expected number of offspring mu over bar satisfies mu over bar <=rho-1. Benjamini and Muller (Groups Geom Dyn, 6:231-247, 2012) conjectured that throughout the transient supercritical phase 1
