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作者：Kendall, Wilfrid S.
作者单位：University of Warwick
摘要：It is shown how to construct a successful co-adapted coupling of two copies of an n-dimensional Brownian motion (B-1,..., B-n) while simultaneously coupling all corresponding copies of Levy stochastic areas integral B-i d B-j - integral B-j dB(i). It is conjectured that successful co-adapted couplings still exist when the Levy stochastic areas are replaced by a finite set of multiply iterated path- and time-integrals, subject to algebraic compatibility of the initial conditions.
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作者：Kaj, Ingemar; Leskela, Lasse; Norros, Ilkka; Schmidt, Volker
作者单位：Uppsala University; Aalto University; Ulm University
摘要：This paper studies the limits of a spatial random field generated by uniformly scattered random sets, as the density lambda of the sets grows to infinity and the mean volume rho of the sets tends to zero. Assuming that the volume distribution has a regularly varying tail with infinite variance, we show that the centered and renormalized random field can have three different limits, depending on the relative speed at which lambda and rho are scaled. If lambda grows much faster than rho shrinks,...
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作者：Barany, Imre; Vu, Van
作者单位：Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; University of London; University College London; Rutgers University System; Rutgers University New Brunswick
摘要：Choose n random, independent points in R-d according to the standard normal distribution. Their convex hull K-n is the Gaussian random polytope. We prove that the volume and the number of faces of K-n satisfy the central limit theorem, settling a well-known conjecture in the field.
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作者：Aldous, David
作者单位：University of California System; University of California Berkeley
摘要：Consider routing traffic on the N x N torus, simultaneously between all source-destination pairs, to minimize the cost Sigma e c(e)f(2) (e), where f (e) is the volume of flow across edge e and the c(e) form an i.i.d. random environment. We prove existence of a rescaled N -> infinity limit constant for minimum cost, by comparison with an appropriate analogous problem about minimum-cost flows across a M x M subsquare of the lattice.
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作者：Guionnet, Alice; Maurel-Segala, Edouard
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We study several-matrix models and show that when the potential is convex and a small perturbation of the Gaussian potential, the first order correction to the free energy can be expressed as a generating function for the enumeration of maps of genus one. In order to do that, we prove a central limit theorem for traces of words of the weakly interacting random matrices defined by these matrix models and show that the variance is a generating function for the number of planar maps with two vert...
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作者：Debussche, Arnaud; Zambotti, Lorenzo
作者单位：Universite Paris Cite; Sorbonne Universite
摘要：We consider a stochastic partial differential equation with reflection at 0 and with the constraint of conservation of the space average. The equation is driven by the derivative in space of a space-time white noise and contains a double Laplacian in the drift. Due to the lack of the maximum principle for the double Laplacian, the standard techniques based on the penalization method do not yield existence of a solution. We propose a method based on infinite dimensional integration by parts for...
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作者：Rassoul-Agha, Firas; Seppalaineni, Timo
作者单位：Utah System of Higher Education; University of Utah; University of Wisconsin System; University of Wisconsin Madison
摘要：We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. We prove an invariance principle (functional central limit theorem) under almost every fixed environment. The assumptions are nonnestling, at least two spatial dimensions, and a 2 + epsilon moment for the step of the walk uniformly in the environment. The main point behind the invariance principle is that the quenched mean of the walk behaves subdiffusively.
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作者：Birkner, Matthias; Zaehle, Iljana
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Erlangen Nuremberg
摘要：We show that the centred occupation time process of the origin of a system of critical binary branching random walks in dimension d >= 3, started off either from a Poisson field or in equilibrium, when suitably normalized, converges to a Brownian motion in d >= 4. In d = 3, the limit process is a fractional Brownian motion with Hurst parameter 3/4 when starting in equilibrium, and a related Gaussian process when starting from a Poisson field. For (dependent) branching random walks with state d...
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作者：Benjamini, Itai; Gurel-Gurevich, Ori; Lyons, Russell
作者单位：Weizmann Institute of Science; Indiana University System; Indiana University Bloomington
摘要：We show that the edges crossed by a random walk in a network form a recurrent graph a.s. In fact, the same is true when those edges are weighted by the number of crossings.
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作者：El Karoui, Noureddine
作者单位：University of California System; University of California Berkeley
摘要：We consider the asymptotic fluctuation behavior of the largest eigenvalue of certain sample covariance matrices in the asymptotic regime where both dimensions of the corresponding data matrix go to infinity. More precisely, let X be an n x p matrix, and let its rows be i.i.d. complex normal vectors with mean 0 and covariance Sigma p. We show that for a large class of covariance matrices Sigma P, the largest eigenvalue of X*X is asymptotically distributed (after recentering and rescaling) as th...
