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作者：Harris, Simon c.; Palau, Sandra; Pardo, Juan carlos
作者单位：University of Auckland; Universidad Nacional Autonoma de Mexico
摘要：We investigate the genealogy of a sample of k >= 2 particles chosen uniformly without replacement from a population alive at large times in a critical discrete-time Galton-Watson process in a varying environment (GWVE). We will show that subject to an explicit deterministic time-change involving only the mean and variances of the varying offspring distributions, the sample genealogy always converges to the same universal genealogical structure; it has the same tree topology as Kingman's coales...
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作者：Nutz, Marcel; Wang, Ruodu; Zhang, Zhenyuan
作者单位：Columbia University; University of Waterloo; Stanford University
摘要：It is well known that martingale transport plans between marginals mu not equal nu are never given by Monge maps-with the understanding that the map is over the first marginal mu, or forward in time. Here, we change the perspective, with surprising results. We show that any distributions mu, nu in convex order with nu atomless admit a martingale coupling given by a Monge map over the second marginal nu. Namely, we construct a particular coupling called the barcode tingale transports are dense ...
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作者：Dhara, Souvik; Mukherjee, Debankur; Ramanan, Kavita
作者单位：University System of Georgia; Georgia Institute of Technology; Brown University
摘要：For an nxn matrix A(n), the r -> p operator norm is defined as parallel to An parallel to(r -> p):= sup(x is an element of R)(n):parallel to x parallel to r(<= 1)(n)(parallel to A)x parallel to(p) for r,p >= 1. For different choices of r and p, this norm corresponds to key quantities that arise in diverse applications including matrix condition number estimation, clustering of data, and construction of oblivious routing schemes in transportation networks. This article considers r -> p norms of...
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作者：Rutiten, Daan; Mukherjee, Debankur
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：The analysis of large-scale, parallel-server load balancing systems has relied heavily on mean-field analysis. A pivotal assumption for this framework is that servers are exchangeable. However, modern data-centers have data locality constraints, such that tasks of a particular type can only be routed to a small subset of servers. An emerging line of research, therefore, considers load balancing algorithms on bipartite graphs where vertices represent task types and servers, respectively. Due to...
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作者：Appuhamillage, Thilanka; Bokil, Vrushali; Thomann, Enrique; Waymire, Edward; Wood, Brian
作者单位：HSBC Holdings; Oregon State University; Oregon State University
摘要：The failure of a symmetry argument for the Laplace transform of a mul-tivariate density given inAnn. Appld. Probab.21(1) (2011), 183-214 wasneglected in preparation of the first errata (Ann. Appld. Probab.21(5) (2011),2050-2051). The formula for the Laplace transform is corrected in this errata
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作者：Landim, Claudio; Misturini, Ricardo; Sau, Federico
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidade Federal do Rio Grande do Sul; University of Trieste
摘要：Let E-n subset of R-d, n >= 1, be a sequence of finite sets and consider a E-n-valued, irreducible, reversible, continuous-time Markov chain (X-t((n)):t >= 0). Denote by P(R-d) the set of probability measures on R-d and by I-n:P(R-d)->[0,+infinity) the level two large deviations rate functional for X(t )((n))as t ->infinity. We present a general method, based on tools used to prove the metastable behaviour of Markov chains, to derive a full expansion of InIn expressing it as I-n=I-(0)+& sum;(1...
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作者：Abry, Patrice; Boniece, B. cooper; Didier, Gustavo; Wendt, Herwig
作者单位：Universite Paris Cite; Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); Drexel University; Tulane University; Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National Polytechnique de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS)
摘要：In this paper, we characterize the asymptotic and large scale behavior of the eigenvalues of wavelet random matrices in high dimensions. We assume that possibly non-Gaussian, finite-variance p-variate measurements are made of a low-dimensional r-variate (r << p ) fractional stochastic process with noncanonical scaling coordinates and in the presence of additive high- dimensional noise. The measurements are correlated both timewise and between rows. We show that the r largest eigenvalues of the...
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作者：Broutin, Nicolas; Kamcev, Nina; Ugosi, Gabor
作者单位：Sorbonne Universite; Universite Paris Cite; University of Zagreb; ICREA
摘要：We consider random temporal graphs, a version of the classical Erdos- R & eacute;nyi random graph G(n, p) where additionally, each edge has a distinct random time stamp, and connectivity is constrained to sequences of edges with increasing time stamps. We study the asymptotics for the distances in such graphs, mostly in the regime of interest where np is of order log n. We establish the first order asymptotics for the lengths of increasing paths: the lengths of the shortest and longest paths b...
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作者：Chen, Xinxin; Garban, Christophe; Shekhar, Atul
作者单位：Beijing Normal University; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：We give a complete characterization of the domain of attraction of fixed points of branching Brownian motion (BBM) with critical drift. Prior to this classification, we introduce a suitable metric space of locally finite point measures on which we prove 1) that the BBM with critical drift is a well-defined Markov process and 2) that it satisfies the Feller property. Several applications of this characterization are given.
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作者：Cheng, Dan; Xiao, Yimin
作者单位：Arizona State University; Arizona State University-Tempe; Michigan State University
摘要：Let { (X (t), Y(s)) : t is an element of T, s is an element of S } be an R2-valued, centered, unit-variance smooth Gaussian vector field, where T and S are compact rectangles in the Euclidean space. It is shown that, as u -> infinity , the joint excursion probability P{supt is an element of T X (t) >= u, sup s is an element of S Y(s) >= u } can be approximated by E{chi (Au)}, the expected Euler characteristic of the excursion set Au = { (t, s) is an element of T x S : X (t) >= u, Y(s) >= u } ,...
