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作者：Last, Guenter; Nestmann, Franz; Schulte, Matthias
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; Heriot Watt University
摘要：The random connection model is a random graph whose vertices are given by the points of a Poisson process and whose edges are obtained by randomly connecting pairs of Poisson points in a position dependent but independent way. We study first and second order properties of the numbers of components isomorphic to given finite connected graphs. For increasing observation windows in an Euclidean setting we prove qualitative multivariate and quantitative univariate central limit theorems for these ...
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作者：Cai, T. Tony; Jiang, Tiefeng; Li, Xiaoou
作者单位：University of Pennsylvania; University of Minnesota System; University of Minnesota Twin Cities
摘要：Consider a standard white Wishart matrix with parameters n and p. Motivated by applications in high-dimensional statistics and signal processing, we perform asymptotic analysis on the maxima and minima of the eigenvalues of all the m x m principal minors, under the asymptotic regime that n, p, m go to infinity. Asymptotic results concerning extreme eigenvalues of principal minors of real Wigner matrices are also obtained. In addition, we discuss an application of the theoretical results to the...
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作者：Bhattacharya, Bhaswar B.; Mukherjee, Somabha; Mukherjee, Sumit
作者单位：University of Pennsylvania; Columbia University
摘要：Consider the random quadratic form T-n = Sigma(1 <= u<= n) a(uv)X(u)X(v), where ((a(uv)))1(<= u,v <= n) is a {0, 1}-valued symmetric matrix with zeros on the diagonal, and X-1, X-2,..., X-n are i.i.d. Ber(p(n)), with p(n) is an element of (0, 1). In this paper, we prove various characterization theorems about the limiting distribution of T-n, in the sparse regime, where p(n) -> 0 such that E(T-n) = O(1). The main result is a decomposition theorem showing that distributional limits of Tn is the...
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作者：Lambert, Amaury; Pina, Veronica Miro; Schertzer, Emmanuel
作者单位：Universite Paris Cite; Sorbonne Universite; Institut National de la Sante et de la Recherche Medicale (Inserm); Universite PSL; College de France
摘要：We consider a Moran model with recombination in a haploid population of size N. At each birth event, with probability 1-rho R-N the offspring copies one parent's chromosome, and with probability rho R-N she inherits a chromosome that is a mosaic of both parental chromosomes. We assume that at time 0 each individual has her chromosome painted in a different color and we study the color partition of the chromosome that is asymptotically fixed in a large population, when we look at a portion of t...
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作者：Bender, Christian; Schweizer, Nikolaus
作者单位：Saarland University; Tilburg University
摘要：We propose a new least-squares Monte Carlo algorithm for the approximation of conditional expectations in the presence of stochastic derivative weights. The algorithm can serve as a building block for solving dynamic programming equations, which arise, for example, in nonlinear option pricing problems or in probabilistic discretization schemes for fully nonlinear parabolic partial differential equations. Our algorithm can be generically applied when the underlying dynamics stem from an Euler a...
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作者：Castiel, Eyal; Borst, Sem; Miclo, Laurent; Simatos, Florian; Whiting, Phil
作者单位：Universite de Toulouse; Institut Superieur de l'Aeronautique et de l'Espace (ISAE-SUPAERO); Eindhoven University of Technology; Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Macquarie University
摘要：We examine a queue-based random-access algorithm where activation and deactivation rates are adapted as functions of queue lengths. We establish its heavy traffic behavior on a complete interference graph, which turns out to be nonstandard in two respects: (1) the scaling depends on some parameter of the algorithm and is not the N/N-2 scaling usually found in functional central limit theorems; (2) the heavy traffic limit is deterministic. We discuss how this nonstandard behavior arises from th...
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作者：van der Hofstad, Remco; van Leeuwaarden, Johan S. H.; Stegehuis, Clara
作者单位：Eindhoven University of Technology; Tilburg University; University of Twente
摘要：Subgraphs reveal information about the geometry and functionalities of complex networks. For scale-free networks with unbounded degree fluctuations, we obtain the asymptotics of the number of times a small connected graph occurs as a subgraph or as an induced subgraph. We obtain these results by analyzing the configuration model with degree exponent tau epsilon (2, 3) and introducing a novel class of optimization problems. For any given subgraph, the unique optimizer describes the degrees of t...
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作者：Hirsch, Christian; Holmes, Mark; Kleptsyn, Victor
作者单位：University of Groningen; University of Melbourne; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rennes
摘要：We study a class of reinforcement models involving a Poisson process on the vertices of certain infinite graphs G. When a vertex fires, one of the edges incident to that vertex is selected. The edge selection is biased towards edges that have been selected many times previously, and a parameter a governs the strength of this bias. We show that for various graphs (including all graphs of bounded degree), if alpha >> 1 (the very strong reinforcement regime) then the random subgraph consisting of...
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作者：Nejjar, Peter
作者单位：University of Bonn
摘要：We consider the asymmetric simple exclusion process (ASEP) on Z with initial data such that in the large time particle density rho(.) a discontinuity (shock) at the origin is created. At the shock, the value of rho jumps from zero to one, but rho(-epsilon), 1 - rho(epsilon) > 0 for any epsilon > 0. We are interested in the rescaled position of a tagged particle which enters the shock with positive probability. We show that, inside the shock region, the particle position has the KPZ-typical 1/3...
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作者：Hermon, Jonathan; Salez, Justin
作者单位：University of British Columbia; Universite PSL; Universite Paris-Dauphine; Universite PSL
摘要：Introduced by Lu and Yau (Comm. Math. Phys. 156 (1993) 399-433), the martingale decomposition method is a powerful recursive strategy that has produced sharp log-Sobolev inequalities for homogeneous particle systems. However, the intractability of certain covariance terms has so far precluded applications to heterogeneous models. Here we demonstrate that the existence of an appropriate coupling can be exploited to bypass this limitation effortlessly. Our main result is a dimension-free modifie...
