-
作者：Lambert, Amaury; Schertzer, Emmanuel
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Biology (INSB); Universite PSL; College de France; Ecole Normale Superieure (ENS); Institut National de la Sante et de la Recherche Medicale (Inserm)
摘要：The nested Kingman coalescent describes the dynamics of particles (called genes) contained in larger components (called species), where pairs of species coalesce at constant rate and pairs of genes coalesce at constant rate provided they lie within the same species. We prove that starting from rn species, the empirical distribution of species masses (numbers of genes/n) at time t/n converges as n -> infinity to a solution of the deterministic coagulation-transport equation partial derivative(t...
-
作者：Bonis, Thomas
作者单位：Universite Paris Saclay
摘要：We use Stein's method to bound the Wasserstein distance of order 2 between a measure nu and the Gaussian measure using a stochastic process (X-t)(t >= 0) such that X-t is drawn from nu for any t > 0. If the stochastic process (X-t)(t >= 0) satisfies an additional exchangeability assumption, we show it can also be used to obtain bounds onWasserstein distances of any order p >= 1. Using our results, we provide convergence rates for the multi-dimensional central limit theorem in terms of Wasserst...
-
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...
-
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...
-
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 ...
-
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...
-
作者：Schoug, Lukas
作者单位：University of Cambridge
摘要：We study SLE kappa (rho) curves, with kappa and rho chosen so that the curves hit the boundary. More precisely, we study the sets on which the curves collide with the boundary at a prescribed angle and determine the almost sure Hausdorff dimensions of these sets. This is done by studying the moments of the spatial derivatives of the conformal maps g(t), by employing the Girsanov theorem and using imaginary geometry techniques to derive a correlation estimate.
-
作者：Berestycki, Nathanael; Powell, Ellen; Ray, Gourab
作者单位：University of Vienna; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Victoria
摘要：We prove that a random distribution in two dimensions which is conformally invariant and satisfies a natural domain Markov property is a multiple of the Gaussian free field. This result holds subject only to a fourth moment assumption.
-
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.
-
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...
