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作者：El Karoui, Noureddine
作者单位：University of California System; University of California Berkeley
摘要：It has been recently shown that if X is an n x N matrix whose entries are i.i.d. standard complex Gaussian and l(1) is the largest eigenvalue of X*X, there exist sequences m(n,N) and s(n,N) such that (l(1) - m(n,N))/s(n,N) converges in distribution to W-2, the Tracy-Widom law appearing in the study of the Gaussian unitary ensemble. This probability law has a density which is known and computable. The cumulative distribution function of W2 is denoted F-2. In this paper we show that, under the a...
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作者：Cassandro, Marzio; Orlandi, Enza; Picco, Pierre
作者单位：Consiglio Nazionale delle Ricerche (CNR); Istituto Nazionale per la Fisica della Materia (INFM-CNR); Sapienza University Rome; Roma Tre University; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：Estimate (3.39) which appears in the proof of Proposition 3.4 in [Ann. Probab. 27 (1999) 1414-1467] is wrong. We present below a corrected proof which introduces an extra factor 2 in equations (3.34) and (3.35). This has no consequence in the rest of the paper since Proposition 3.4 is used to estimate only ratios; see (3.23) and (3.25).
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作者：Kratz, Marie F.; Leon, Jose R.
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; University of Central Venezuela
摘要：Cramer and Leadbetter introduced in 1967 the sufficient condition r(s)-r(0)/s is an element of L-1([0,delta], dx), delta > 0, to have a finite variance of the number of zeros of a centered stationary Gaussian process with twice differentiable covariance function r. This condition is known as the Geman condition, since Geman proved in 1972 that it was also a necessary condition. Up to now no such criterion was known for counts of crossings of a level other than the mean, This paper shows that t...
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作者：Atar, Rami; Budhiraja, Amarjit
作者单位：Technion Israel Institute of Technology; University of North Carolina; University of North Carolina Chapel Hill
摘要：We study a class of stochastic control problems where a cost of the form E integral([0,infinity)) e(-beta s) [l(X-S)ds + h (Y-S degrees) d vertical bar Y vertical bar(s)] is to be minimized over control processes Y whose increments take values in a cone Y of RP, keeping the state process X = x + B + G Y in a cone X of R-k, k <= p. Here, x c X, B is a Brownian motion with drift b and covariance E, G is a fixed matrix, and Y degrees is the Radon-Nikodym derivative dY vertical bar d vertical bar ...
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作者：Janson, Svante
作者单位：Uppsala University
摘要：We study the characteristic function and moments of the integer-valued random variable [X + alpha], where X is a continuous random variables. The results can be regarded as exact versions of Sheppard's correction. Rounded variables of this type often occur as subsequence limits of sequences of integer-valued random variables. This leads to oscillatory terms in asymptotics for these variables, something that has often been observed, for example in the analysis of several algorithms. We give som...
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作者：Mustapha, S
作者单位：Universite Paris Cite; Sorbonne Universite
摘要：It is shown in this paper that the transition kernel corresponding to a spatially inhomogeneous random walk on Z(d) admits upper and lower Gaussian estimates.
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作者：Chatterjee, Sourav
作者单位：University of California System; University of California Berkeley
摘要：We generalize Lindeberg's proof of the central limit theorem to an invariance principle for arbitrary smooth functions of independent and weakly dependent random variables. The result is applied to get a similar theorem for smooth functions of exchangeable random variables. This theorem allows us to identify, for the first time, the limiting spectral distributions of Wigner matrices with exchangeable entries.
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作者：Gnedin, Alexander V.; Yakubovich, Yuri
作者单位：Utrecht University
摘要：A class of random discrete distributions P is introduced by means of a recursive splitting of unity. Assuming supercritical branching, we show that for partitions induced by sampling from such P a power growth of the number of blocks is typical. Some known and some new partition structures appear when P is induced by a Dirichlet splitting.
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作者：Luczak, Malwina J.; McDiarmid, Colin
作者单位：University of London; London School Economics & Political Science; University of Oxford
摘要：There are n queues, each with a single server. Customers arrive in a Poisson process at rate lambda n, where 0 < lambda < 1. Upon arrival each customer selects d >= 2 servers uniformly at random, and joins the queue at a least-loaded server among those chosen. Service times are independent exponentially distributed random variables with mean 1. We show that the system is rapidly mixing, and then investigate the maximum length of a queue in the equilibrium distribution. We prove that with proba...
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作者：Bryc, W; Dembo, A; Jiang, TF
作者单位：University System of Ohio; University of Cincinnati; Stanford University; Stanford University; University of Minnesota System; University of Minnesota Twin Cities
摘要：We study the limiting spectral measure of large symmetric random matrices of linear algebraic structure. For Hankel and Toeplitz matrices generated by i.i.d. random variables {X-k} of unit variance, and for symmetric Markov matrices generated by i.i.d. random variables {X-ij} (j > i) of zero mean and unit variance, scaling the eigen-values by root n we prove the almost sure, weak convergence of the spectral measures to universal, nonrandom, symmetric distributions gamma(H), gamma(M) and gamma(...
