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作者：Letac, G; Wesolowski, J
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Warsaw University of Technology; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; University of Warsaw
摘要：Matsumoto and Yor have recently discovered an interesting transformation which preserves a bivariate probability measure which is a product of the generalized inverse Gaussian (GIG) and gamma distributions. This paper is devoted to a detailed study of this phenomenon. Let X and Y be two independent positive random variables. We prove (Theorem 4.1) that U = (X + Y)(-1) and V = X-1 - (X + Y)(-1) are independent if and only if there exists p, a, b > 0 such that Y is gamma distributed with shape p...
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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：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...
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作者：Bruss, FT
作者单位：Universite Libre de Bruxelles
摘要：The objective of this paper is to present two theorems which are directly applicable to optimal stopping problems involving independent indicator functions. The proofs are elementary. One implication of the results is a convenient solution algorithm to obtain the optimal stopping rule and the value. We will apply it to several examples of sequences of independent indicators, including sequences of random length. Another interesting implication of the results is that the in well-known asymptoti...
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作者：Sudbury, A
摘要：We consider interacting particle systems on Z which allow five types of pairwise interaction: Annihilation, Birth, Coalescence, Death and Exclusion with corresponding rates a, b, c, d, e. We show that whatever the values of a, c, d, e, if the birthrate is high enough there is a positive probability the particle system will survive starting from airy finite occupied set. In particular: an IFS with rates a, b, c, d, e has a positive probability of survival if b > 4d + 6a, c + a greater than or e...
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作者：Merlevède, F; Peligrad, M
作者单位：Sorbonne Universite; University System of Ohio; University of Cincinnati
摘要：We prove a central limit theorem for strongly mixing sequences under a sharp sufficient condition which combines the rate of the strong mixing coefficient with the quantile function. The result improves on all earlier central limit theorems for this type of dependence and answers a conjecture raised by Bradley in 1997. Moreover, we derive the corresponding functional central limit theorem.
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作者：Soshnikov, A
作者单位：California Institute of Technology; University of California System; University of California Davis
摘要：We discuss the CLT for the global and local linear statistics of random matrices from classical compact groups. The main parts of our proofs are certain combinatorial identities, much in the spirit of works by M. Kac and H. Spohn.
