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作者：Wieand, K
作者单位：University of Arizona
摘要：Let M be a randomly chosen n x n permutation matrix. For a fixed are of the unit circle, let X be the number of eigenvalues of M which lie in the specified are. We calculate the large n asymptotics for the mean and variance of X, and show that (X - E[X])/(Var(X))(1/2) is asymptotically normally distributed. In addition, we show that for several fixed arcs I-1,...,I-m, the corresponding random variables are jointly normal in the large n limit.
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作者：Chen, MF; Wang, FY
作者单位：Beijing Normal University
摘要：In this paper, some new forms of Cheeger's inequalities are established for general (maybe unbounded) symmetric forms (Theorems 1.1 and 1.2): the resulting estimates improve and extend the ones obtained by Lawler and Sokal for bounded jump processes. Furthermore, some existence criteria for spectral gap of general symmetric forms or general reversible Markov processes are presented (Theorems 1.4 and 3.1), based on Cheeger's inequalities and a relationship between the spectral gap and the first...
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作者：Wang, QY; Jing, BY; Zhao, LC
作者单位：University of Wollongong; Hong Kong University of Science & Technology; Chinese Academy of Sciences; University of Science & Technology of China, CAS
摘要：We derive Berry-Esseen bounds for a class of Studentized statistics. The results are applied to Studentized U-statistics, Studentized L-statistics and Studentized functions of the sample mean to give the Berry-Esseen bounds under conditions weaker than those obtained by alternative methods.
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作者：Talagrand, M
作者单位：Sorbonne Universite
摘要：We provide an extremely accurate picture of the Sherrington-Kirkpatrick model in three cases: for high temperature, for large external field and for any temperature greater than or equal to 1 and sufficiently small external field. We describe the system at the level of the central limit theorem, or as physicists would say, at the level of fluctuations around the mean field. We also obtain much more detailed information, in the form of exponential inequalities that express a uniform control ove...
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作者：Kenyon, R
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
摘要：Let U be a multiply connected region in R-2 with smooth boundary. Let P-epsilon be a polyomino in epsilonZ(2) approximating U as epsilon --> 0. We show that, for certain boundary conditions on P-epsilon, the height distribution on a random domino tiling (dimer covering) of P-epsilon is conformally invariant in the limit as epsilon tends to 0, in the sense that the distribution of heights of boundary components (or rather, the difference of the heights from their mean values) only depends on th...
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作者：Massart, P
作者单位：Universite Paris Saclay
摘要：We propose some explicit values for the constants involved in the exponential concentration inequalities for empirical processes which are due to Talagrand. It has been shown by Ledoux that deviation inequalities for empirical processes could be obtained by iteration of logarithmic Sobolev type inequalities. Our approach follows closely that of Ledoux. The improvements that we get with respect to Ledoux's work are based on refinements of his entropy inequalities and computations.
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作者：Gut, A; Spataru, A
作者单位：Uppsala University; Romanian Academy; Institute of Mathematical Statistics & Applied Mathematics of Romanian Academy
摘要：Let X, X-1, X-2,... be i.i.d. random variables with mean 0 and positive, finite variance sigma (2), and set S-n = X-1 + ... + X-n, n greater than or equal to 1. Continuing earlier work related to strong laws, we prove the following analogs for the law of the iterated logarithm: lim(epsilon down arrow sigma root2) root epsilon (2)-2 sigma (2) Sigma (n greater than or equal to3) 1/n P(\S-n\ greater than or equal to epsilon rootn log log n + a(n)) = sigma root2 whenever a(n) = O(rootn(log log n)(...
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作者：Rosinski, J
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：This work is concerned with the structural analysis of stationary alpha -stable random fields. Three distinct classes of such random fields are characterized and it is shown that every stationary alpha -stable random field can be uniquely decomposed into the sum of three independent components belonging to these classes. Various examples of stationary alpha -stable random fields are discussed in this context.
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作者：Talagrand, B
作者单位：Sorbonne Universite; University System of Ohio; Ohio State University
摘要：In a previous work, we proved the validity of the replica-symmetric solution for the Hopfield model in a nontrivial domain of parameters. This was done at the accuracy of the LLN. In a somewhat larger domain, we obtain a description at the level of the CLT, or, in the terminology of physics, we calculate the fluctuations around the mean field. This is obtained by refining the tools we developed for a rigorous use of the cavity method and proving new a priori estimates about the localization of...
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作者：Bentkus, V; Juozulynas, A; Paulauskas, V
作者单位：Vilnius University; Vilnius University
摘要：The standard normal distribution Phi on R-d satisfies Phi ((partial derivativeC)(epsilon)) less than or equal to c(d)epsilon, for all epsilon > 0 and for all convex subsets C subset of R-d, with a constant c(d) which depends on the dimension d only. Here partial derivativeC denotes the boundary of C, and (partial derivativeC)(epsilon) stands for the epsilon -neighborhood of partial derivativeC. Such bounds for the normal measure of convex shells are extensively used to estimate the accuracy of...
