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作者：Kang, W. N.; Kelly, F. P.; Lee, N. H.; Williams, R. J.
作者单位：Carnegie Mellon University; University of Cambridge; Johns Hopkins University; University of California System; University of California San Diego
摘要：We consider a connection-level model of Internet congestion control, introduced by Massoulie and Roberts [Telecommunication Systems 15 (2000) 185-201], that represents the randomly varying number of flows present in a network. Here, bandwidth is shared fairly among elastic document transfers according to a weighted a-fair bandwidth sharing policy introduced by Mo and Walrand [IEEE/ACM Transactions on Networking 8 (2000) 556-567] [alpha is an element of (0, infinity)]. Assuming Poisson arrivals...
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作者：Woodard, Dawn B.; Schmidler, Scott C.; Huber, Mark
作者单位：Duke University; Duke University
摘要：We give conditions under which a Markov chain constructed via parallel or simulated tempering is guaranteed to be rapidly mixing, which are applicable to a wide range of multimodal distributions arising in Bayesian statistical inference and statistical mechanics. We provide lower bounds on the spectral gaps of parallel and simulated tempering. These bounds imply a single set of sufficient conditions for rapid mixing of both techniques. A direct consequence of our results is rapid mixing of par...
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作者：Gnedin, Alexander V.; Iksanov, Alexander M.; Negadajlov, Pavlo; Roesler, Uwe
作者单位：Utrecht University; University of Kiel
摘要：We consider an occupancy scheme in which balls are identified with n points sampled from the standard exponential distribution, while the role of boxes is played by the spacings induced by an independent random walk with positive and nonlattice steps. We discuss the asymptotic behavior of five quantities: the index K-n* of the last occupied box, the number K-n of occupied boxes, the number K-n,K-0 of empty boxes whose index is at most K-n*, the index W-n of the first empty box and the number o...
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作者：Dyer, Martin; Goldberg, Leslie Ann; Jerrum, Mark
作者单位：University of Leeds; University of Liverpool; University of London
摘要：We give a systematic development of the application of matrix norms to rapid mixing in spin systems. We show that rapid mixing of both random update Glauber dynamics and systematic scan Glauber dynamics occurs if any matrix norm or the associated dependency matrix is less than 1. We give improved analysis for the case in which the diagonal of the dependency matrix is 0 (as in heat bath dynamics). We apply the matrix norm methods to random update and systematic scan Glauber dynamics for colorin...
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作者：Graham, Benjamin T.
作者单位：University of British Columbia
摘要：We study the zero-range process on the complete graph. It is a Markov chain model for a microcanonical ensemble. We prove that the process converges to a fluid limit. The fluid limit rapidly relaxes to the appropriate Gibbs distribution.
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作者：Collet, P.; Giardina, C.; Redig, F.
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Physics (INP); Institut Polytechnique de Paris; Ecole Polytechnique; Eindhoven University of Technology; Leiden University - Excl LUMC; Leiden University
摘要：We consider matching with shifts for Gibbsian sequences. We prove that the maximal overlap behaves as clog it, where c is explicitly identified in terms of the thermodynamic quantities (pressure) of the underlying potential. Our approach is based on the analysis of the first and second moment of the number of overlaps of a given size. We treat both the case of equal sequences (and nonzero shifts) and independent sequences.
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作者：Del Moral, Pierre; Patras, Frederic; Rubenthaler, Sylvain
作者单位：Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Inria; Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur
摘要：We design exact polynomial expansions of a class of Feynman-Kac particle distributions. These expansions are finite and are parametrized by coalescent trees and other related combinatorial quantities. The accuracy of the expansions at any order is related naturally to the number of coalescences of the trees. Our results include an extension of the Wick product formula to interacting particle systems. They also provide refined nonasymptotic propagation of chaos-type properties, as well as sharp...
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作者：Garet, Olivier
作者单位：Universite de Lorraine
摘要：This paper concerns maximal flows on Z(2) traveling from a convex set to infinity, the flows being restricted by a random capacity. For every compact convex set A, we prove that the maximal flow Phi(nA) between nA and infinity is such that Phi(nA)/n it almost surely converges to the integral of a deterministic function over the boundary of A. The limit can also be interpreted as the optimum of a deterministic continuous max-flow problem. We derive some properties of the infinite cluster in sup...
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作者：Khare, Kshitij; Zhou, Hua
作者单位：Stanford University; University of California System; University of California Los Angeles; University of California Los Angeles Medical Center; David Geffen School of Medicine at UCLA
摘要：We provide a sharp nonasymptotic analysis of the rates of convergence for some standard multivariate Markov chains using spectral techniques. All chains under consideration have multivariate orthogonal polynomial as eigenfunctions. Our examples include the Moran model in population genetics and its variants in community ecology, the Dirichlet-multinomial Gibbs sampler, a class of generalized Bernoulli-Laplace processes, a generalized Ehrenfest urn model and the multivariate normal autoregressi...
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作者：Yakovlev, Andrei Y.; Yanev, Nikolay M.
作者单位：University of Rochester; Bulgarian Academy of Sciences
摘要：This paper considers the relative frequencies of distinct types of individuals in multitype branching processes. We prove that the frequencies are asymptotically multivariate normal when the initial number of ancestors is large and the time of observation is fixed. The result is valid for any branching process with a finite number of types; the only assumption required is that of independent individual evolutions. The problem under consideration is motivated by applications in the area of cell...
