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作者：Arapostathis, Ari; Pang, Guodong
作者单位：University of Texas System; University of Texas Austin; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：We consider Markovian multiclass multi-pool networks with heterogeneous server pools, each consisting of many statistically identical parallel servers, where the bipartite graph of customer classes and server pools forms a tree. Customers form their own queue and are served in the first-come first served discipline, and can abandon while waiting in queue. Service rates are both class and pool dependent. The objective is to study the limiting diffusion control problems under the long run averag...
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作者：Cerny, Jeri; Teixeira, Augusto
作者单位：University of Vienna
摘要：For d >= 3, we construct a new coupling of the trace left by a random walk on a large d-dimensional discrete torus with the random interlacements on Z(d). This coupling has the advantage of working up to macroscopic subsets of the torus. As an application, we show a sharp phase transition for the diameter of the component of the vacant set on the torus containing a given point. The threshold where this phase transition takes place coincides with the critical value u star(d) of random interlace...
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作者：Zhang, Xicheng
作者单位：Wuhan University
摘要：In this paper, we study properties of solutions to stochastic differential equations with Sobolev diffusion coefficients and singular drifts. The properties we study include stability with respect to the coefficients, weak differentiability with respect to starting points and the Malliavin differentiability with respect to sample paths. We also establish Bismut-Elworthy-Li's formula for the solutions. As an application, we use the stochastic Lagrangian representation of incompressible Navier-S...
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作者：Martinsson, Anders
作者单位：Chalmers University of Technology; University of Gothenburg
摘要：The n-dimensional binary hypercube is the graph whose vertices are the binary n-tuples {0,1)(n) and where two vertices are connected by an edge if they differ at exactly one coordinate. We prove that if the edges are assigned independent mean 1 exponential costs, the minimum length T-n of a path from (0,0,..., 0) to (1,1,, 1) converges in probability to ln(1 + root 2) approximate to 0.881. It has previously been shown by Fill and Pemantle [Ann. Appl. Probab. 3 (1993) 593-629] that this so-call...
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作者：Sun, Wen; Feuillet, Mathieu; Robert, Philippe
摘要：In this paper, a stochastic model of a large distributed system where users' files are duplicated on unreliable data servers is investigated. Due to a server breakdown, a copy of a file can be lost, it can be retrieved if another copy of the same file is stored on other servers. In the case where no other copy of a given file is present in the network, it is definitively lost. In order to have multiple copies of a given file, it is assumed that each server can devote a fraction of its processi...
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作者：Broutin, Nicolas; Devroye, Luc; Lugosi, Gabor
作者单位：McGill University; Pompeu Fabra University
摘要：A random geometric irrigation graph Gamma(n)(r(n), xi) has n vertices identified by n independent uniformly distributed points X-1, ..., X-n in the unit square [0, 11(2). Each point X-i selects xi(i) neighbors at random, without replacement, among those points X-i (j not equal i) for which parallel to X-i - X-j parallel to < r(n), and the selected vertices are connected to X-i by an edge. The number xi(i) of the neighbors is an integer-valued random variable, chosen independently with identica...
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作者：Jaisson, Thibault; Rosenbaum, Mathieu
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Sorbonne Universite
摘要：We investigate the asymptotic behavior as time goes to infinity of Hawkes processes whose regression kernel has L-1 norm close to one and power law tail of the form x(-(1+alpha)), with alpha is an element of (0, 1). We in particular prove that when alpha is an element of (1/2, 1), after suitable rescaling, their law asymptotically behaves as a kind of integrated fractional Cox Ingersoll Ross process, with associated Hurst parameter H = alpha - 1/2. This result is in contrast to the case of a r...
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作者：Hwang, Sung Jin; Damelin, Steven B.; Hero, Alfred O., III
作者单位：University of Michigan System; University of Michigan
摘要：Let (M, g(1)) be a complete d-dimensional Riemannian manifold for d > 1. Let X-n be a set of n sample points in M drawn randomly from a smooth Lebesgue density f supported in M. Let x, y be two points in M. We prove that the normalized length of the power-weighted shortest path between x, y through X-n converges almost surely to a constant multiple of the Riemannian distance between x, y under the metric tensor g(p) = f(2)(1-P)/d g(1), where p > 1 is the power parameter.
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作者：Kanzieper, Eugene; Poplavskyi, Mihail; Timm, Carsten; Tribe, Roger; Zaboronski, Oleg
作者单位：Weizmann Institute of Science; University of Warwick; Technische Universitat Dresden
摘要：We study the large-n limit of the probability P-2n,P-2k that a random 2n x 2n matrix sampled from the real Ginibre ensemble has 2k real eigenvalues. We prove that lim(n ->infinity)1/root 2n log P-2n,P-2k = lim(n ->infinity) 1/root 2n log P-2n,P-0 = -1/root 2 pi zeta (3/2), where zeta is the Riemann zeta-function. Moreover, for any sequence of non-negative integers (k(n))(n >= 1), lim(n ->infinity) 1/root 2n log p(2n,2kn) = -1/root 2 pi zeta (3/2), provided lim(n ->infinity) (n(-1/2) log(n))k(n...
