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作者：BAI, ZD
摘要：In the first part of the paper, we developed certain inequalities to bound the difference between distributions in terms of their Stieltjes transforms and established a convergence rate of expected spectral distributions of large Wigner matrices. The second part is devoted to establishing convergence rates for the sample covariance matrices, for the cases where the ratio of the dimension to the degrees of freedom is bounded away from 1 or close to 1, respectively.
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作者：TALAGRAND, M
作者单位：University System of Ohio; Ohio State University
摘要：We develop new tools that enable us to extend the majorizing measure lower bound to a large class of infinitely divisible processes. We show (in a rigorous sense) that the complexity of these processes is dominated by the complexity of the positive infinitely divisible processes.
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作者：ENCHEV, O
摘要：We study shift transformations on a general abstract Wiener space (E, H, mu), which have the form: E contains omega --> T(phi)omega equivalent to omega - integral(0)(T) phi(t)(omega)Z(dt) is an element of E, where phi(t)(omega) is a scalar function on [0,T] x E and Z is an orthogonal H-valued measure. Under suitable conditions for the kernel phi, we construct explicitly a probability measure mu(phi) on E, which is equivalent to the standard Wiener measure mu and has the property: mu(phi){T-phi...
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作者：ACCARDI, L; LU, YG
摘要：A continuous version of De Finetti's theorem is proved in which the role of the homogeneous product states is played by the independent increment stationary processes on the real line. The proof is based on a conditional, finite De Finetti's theorem (i.e., a result involving only a finite number of random variables and exchangeable conditional expectations rather than exchangeable probabilities). Our technique of proof improves and simplifies a result of Freedman and includes a generalization ...
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作者：CARLSON, JM; GRANNAN, ER; SWINDLE, GH; TOUR, J
作者单位：University of California System; University of California Santa Barbara; AT&T; Nokia Corporation; Nokia Bell Labs; University of California System; University of California Los Angeles
摘要：We establish hydrodynamic limits for a class of attractive, reversible particle systems with an infinite range of interaction. The limiting nonlinear diffusion equations have diffusion coefficients which are functions of the local density, and which have a singularity at a critical value of the density. On open driven systems, these singular diffusion limits explain the observed nontrivial scaling behavior known as self-organized criticality.
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作者：INGLOT, T; LEDWINA, T
摘要：Let alpha(n) be the classical empirical process. Assume T, defined on D[0, 1], satisfies the Lipschitz condition with respect to a weighted sup-norm in D[0, 1]. Explicit bounds for P(T(alpha(n)) greater-than-or-equal-to x(n) square-root n) are obtained for every n greater-than-or-equal-to n0 and all x(n) is-an-element-of (0, sigma], where n0 and sigma are also explicitly given. These bounds lead to moderately large deviations and expansions of the asymptotic large deviations for T(alpha(n)). T...
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作者：MOGULSKII, AA
摘要：This PaPer strengthens and generalizes some theorems proved earlier by Lynch and Sethuraman on large deviations (LD) for random processes with independent increments.
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作者：LALLEY, SP
摘要：Local limit theorems and saddlepoint approximations are given for random walks on a free group whose step distributions have finite support. The techniques used to prove these results are necessarily different from those used for random walks in Euclidean spaces, because Fourier analysis is not available; the basic tools are the elementary theory of algebraic functions and the Perron-Frobenius theory of nonnegative matrices. An application to the structure of the boundary process is also given.
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作者：PRAESTGAARD, J; WELLNER, JA
作者单位：University of Washington; University of Washington Seattle
摘要：We consider an exchangeably weighted bootstrap of the general function-indexed empirical process. We find sufficient conditions on the bootstrap weights for the central limit theorem to hold for the bootstrapped empirical process, almost surely and in probability. The results resemble those of Gine and Zinn for Efron's bootstrap. As a corollary we obtain a result on the almost sure convergence in distribution of the Efron-bootstrapped empirical process with arbitrary sample size. A large numbe...
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作者：DINWOODIE, IH
摘要：Assume a sequence of probabilities {P(n)} has a large deviation rate function I. It is proved that I takes a form analogous to a convex conjugate. If I is also assumed convex, then I is a convex conjugate of an explicitly defined function psi. The results are applied to the empirical law of a Markov chain yielding universal bounds on I. Examples are given of Markov chains in which the empirical law has a large deviation rate strictly between the given bounds.
