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作者：Jammalamadaka, Sreenivasa Rao; Janson, Svante
作者单位：University of California System; University of California Santa Barbara; Uppsala University
摘要：Extreme value theory is part and parcel of any study of order statistics in one dimension. Our aim here is to consider such large sample theory for the maximum distance to the origin, and the related maximum interpoint distance,'' in multidimensions. We show that for a family of spherically symmetric distributions, these statistics have a Gumbel-type limit, generalizing several existing results. We also discuss the other two types of limit laws and suggest some open problems. This work complem...
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作者：Bayraktar, Erhan; Nadtochiy, Sergey
作者单位：University of Michigan System; University of Michigan
摘要：In this paper, we develop a new mathematical technique which allows us to express the joint distribution of a Markov process and its running maximum (or minimum) through the marginal distribution of the process itself. This technique is an extension of the classical reflection principle for Brownian motion, and it is obtained by weakening the assumptions of symmetry required for the classical reflection principle to work. We call this method a weak reflection principle and show that it provide...
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作者：Verzelen, Nicolas; Arias-Castro, Ery
作者单位：INRAE; University of California System; University of California San Diego
摘要：We consider the problem of detecting a tight community in a sparse random network. This is formalized as testing for the existence of a dense random subgraph in a random graph. Under the null hypothesis, the graph is a realization of an Erdos-Renyi graph on N vertices and with connection probability p(0); under the alternative, there is an unknown subgraph on n vertices where the connection probability is p(1) > p(0). In Arias-Castro and Verzelen [Ann. Statist. 42 (2014) 940- 969], we focused ...
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作者：Zhang, Hongzhong; Rodosthenous, Neofytos; Hadjiliadis, Olympia
作者单位：Columbia University; University of London; Queen Mary University London; City University of New York (CUNY) System; Hunter College (CUNY); City University of New York (CUNY) System; City University of New York (CUNY) System
摘要：We study a Wiener disorder problem of detecting the minimum of N change-points in N observation channels coupled by correlated noises. It is assumed that the observations in each dimension can have different strengths and that the change-points may differ from channel to channel. The objective is the quickest detection of the minimum of the N change-points. We adopt a min-max approach and consider an extended Lorden's criterion, which is minimized subject to a constraint on the mean time to th...
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作者：Blanchet, Jose; Chen, Xinyun
作者单位：Columbia University; State University of New York (SUNY) System; Stony Brook University
摘要：This paper develops the first class of algorithms that enable unbiased estimation of steady-state expectations for multidimensional reflected Brownian motion. In order to explain our ideas, we first consider the case of compound Poisson (possibly Markov modulated) input. In this case, we analyze the complexity of our procedure as the dimension of the network increases and show that, under certain assumptions, the algorithm has polynomial-expected termination time. Our methodology includes proc...
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作者：Arapstathis, Art; Biswas, Anup; 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 study a dynamic scheduling problem for a multi-class queueing network with a large pool of statistically identical servers. The arrival processes are Poisson, and service times and patience times are assumed to be exponentially distributed and class dependent. The optimization criterion is the expected long time average (ergodic) of a general (nonlinear) running cost function of the queue lengths. We consider this control problem in the Halfin-Whitt (QED) regime, that is, the number of serv...
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作者：Wang, Chen; Jin, Baisuo; Bai, Z. D.; Nair, K. Krishnan; Harding, Matthew
作者单位：National University of Singapore; Chinese Academy of Sciences; University of Science & Technology of China, CAS; Northeast Normal University - China; Northeast Normal University - China; Stanford University; Duke University
摘要：The auto-cross covariance matrix is defined as M-n = 1/2T Sigma(T)(j=1) (e(j)e(j+pi)* + e(j+tau)e(j)*), where e(j)'s are n-dimensional vectors of independent standard complex components with a common mean 0, variance sigma(2), and uniformly bounded 2 + eta th moments and tau is the lag. Jin et al. [Ann. AppL Probab. 24 (2014) 119912251 has proved that the LSD of M-n exists uniquely and nonrandomly, and independent of tau for all tau >= 1. And in addition they gave an analytic expression of the...
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作者：Muller, Tobias; Spoehel, Reto
作者单位：Utrecht University
摘要：The random geometric graph is obtained by sampling n points from the unit square (uniformly at random and independently), and connecting two points whenever their distance is at most r, for some given r = r(n). We consider the following variation on the random geometric graph: in each of n rounds in total, a player is offered two random points from the unit square, and has to select exactly one of these two points for inclusion in the evolving geometric graph. We study the problem of avoiding ...
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作者：Yogeshwaran, D.; Adler, Robert J.
作者单位：Indian Statistical Institute; Indian Statistical Institute Bangalore; Technion Israel Institute of Technology
摘要：There has been considerable recent interest, primarily motivated by problems in applied algebraic topology, in the homology of random simplicial complexes. We consider the scenario in which the vertices of the simplices are the points of a random point process in R-d, and the edges and faces are determined according to some deterministic rule, typically leading to Cech and Vietoris-Rips complexes. In particular, we obtain results about homology, as measured via the growth of Beth numbers, when...
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作者：Durrett, Rick; Zhang, Yuan
作者单位：Duke University
摘要：In this paper, we consider two attractive stochastic spatial models in which each site can be in state 0, 1 or 2: Krone's model in which 0 = vacant, 1 = juvenile and 2 = a mature individual capable of giving birth, and the Staver-Levin forest model in which 0 = grass, 1 = sapling and 2 = tree. Our first result shows that if (0, 0) is an unstable fixed point of the mean-field ODE for densities of 1's and 2's then when the range of interaction is large, there is positive probability of survival ...
