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作者：Feng, S; Hoppe, FM
作者单位：McMaster University
摘要：Large deviation principles are established for some random combinatorial structures including the Ewens sampling formula and the Pitman sampling formula. A path-level large deviation principle is established for the former on the cadlag space D([0, 1], R) equipped with the uniform convergence topology, and the rate function is the same as for a Poisson process justifying the Poisson process approximation for the Ewens sampling formula at the large deviation level. A large deviation principle f...
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作者：Massey, WA; Whitt, W
作者单位：Nokia Corporation; Nokia Bell Labs; Alcatel-Lucent; Lucent Technologies; AT&T; AT&T
摘要：We study uniform acceleration (UA) expansions of finite-state continuous-time Markov chains with time-varying transition rates. The UA expansions can be used to justify evaluate and reline the pointwise stationary approximation, which is the steady-state distribution associated with the time-dependent generator at the time of interest. We obtain UA approximations from these UA asymptotic expansions. We derive a time-varying analog to the uniformization representation of transition probabilitie...
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作者：Bertsimas, D; Paschalidis, IC; Tsitsiklis, JN
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Boston University
摘要：We consider a single class, acyclic network of G/G/1 queues. We impose some mild assumptions on the service and external arrival processes and we characterize the large deviations behavior of all the processes resulting from various operations in the network. For the network model that we are considering, these operations are passing-through-a-single-server-queue (the process resulting from this operation being the departure process), superposition of independent processes and deterministic sp...
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作者：Ciucu, M
作者单位：Institute for Advanced Study - USA
摘要：We consider the following problem. A deck of 2n cards labeled consecutively from 1 on top to 2n on bottom is face down on the table. The deck is given k dovetail shuffles and placed back on the table, face down. A guesser tries to guess at the cards one at a time, starting from top. The identity of the card guessed at is not revealed, nor is the guesser told whether a particular guess was correct or not. The goal is to maximize the number of correct guesses. We show that, for k greater than or...
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作者：Asselah, A
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider nonreversible exchange dynamics in Z(d) and prove that the stationary, translation invariant measures satisfy the following property: if one of them is a Gibbs measure with a summable potential {J(R), R subset of Z(d)}, then all of them are convex combinations of Gibbs measures with the same potential, but different chemical potentials J({0}).
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作者：Resnick, S; Starica, C
作者单位：Cornell University; University of Pennsylvania
摘要：A popular estimator of the index of regular variation in heavy-tailed models is Hill's estimator. We discuss the consistency of estimator when it is applied to certain classes of heavy-tailed stationary processes. One class of processes discussed consists of processes which can be appropriately approximated by sequences of m-dependent, random variables and special cases of our results show the consistency of Hill's estimator for (i) infinite moving averages with heavy-tail innovations, (ii) a ...
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作者：Roberts, GO; Rosenthal, JS
作者单位：University of Cambridge; University of Toronto
摘要：We consider a Gibbs sampler applied to the uniform distribution on a bounded region R subset of or equal to R-d. We show that the convergence properties of the Gibbs sampler depend greatly on the smoothness of the boundary of R. Indeed, for sufficiently smooth boundaries the sampler is uniformly ergodic, while for jagged boundaries the sampler could fail to even be geometrically ergodic.
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作者：Ramanan, K; Dupuis, P
作者单位：Brown University
摘要：Using large deviation techniques, we analyze the tail behavior of the stationary distribution of the buffer content process for a two-station communication network. We also show how the associated rate function can be expressed as the solution to a finite-dimensional variational problem. Along the way, we develop a number of results and techniques that are of independent interest, including continuity results for the input-output mapping for certain multiclass fluid models and a new technique ...
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作者：Duffield, NG; Whitt, W
作者单位：AT&T
摘要：We show, under regularity conditions, that a nonnegative nondecreasing real-valued stochastic process satisfies a large deviation principle (LDP) with nonlinear scaling if and only if its inverse process does. We also determine how the associated scaling and rate functions must be related. A key condition for the LDP equivalence is for the composition of two of the scaling functions to be regularly varying with nonnegative index. We apply the LDP equivalence to develop equivalent characterizat...
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作者：Löwe, M
作者单位：University of Bielefeld
摘要：We analyze the storage capacity of the Hopfield model with correlated patterns (xi(i)(nu)). We treat both the case of semantically and spatially correlated patterns (i.e., the patterns are either correlated in nu but independent in i or vice versa). We show that the standard Hopfield model of neural networks with N neurons can store N/(gamma logN) or alpha N correlated patterns (depending on which notion of storage is used), provided that the correlation comes from a homogeneous Markov chain. ...
