LARGE DEVIATIONS FOR TOP EIGENVALUES OF β-JACOBI ENSEMBLES AT SCALING TEMPERATURES

Let λ=(λ₁,…,λ_n) be β-Jacobi ensembles with parameters p₁,p₂,n and β,with β varying with n.Set■.Suppose that■ and 0 ≤σγ <1.We offer the large deviation for p₁+p₂/p₁■ λ_i when γ> 0 via the large deviation of the corresponding empirical measure and via a direct estimate,respectively,when γ=0.     

β-Hermite系综关于β-Laguerre系综的逼近

本文研究了β-Hermite系综关于β-Laguerre系综在Kullback-Leibler距离和全变差距离下逼近的问题.利用Pinsker不等式和β-Hermite系综的中心极限定理以及β-Laguerre系综的三阶矩,我们获得了两种距离下逼近的充要条件.此结果推广了文献[4]中的结果.     

TRANSPORTATION INEQUALITIES FOR WEAKLY DEPENDENT SEQUENCES

In [3], they gave necessary and sufficient condition for T 1 C and then as applications T 1 C for weakly dependent sequences was established. In this note, based on Gozlan-L′eonard characterization for W 1 H -inequalities, we extends this result to W 1 H inequalities.     

CONVEX CONCENTRATION INEQUALITIES FOR CONTINUOUS GAS AND STOCHASTIC DOMINATION

In this article, we consider the continuous gas in a bounded domain ∧ of R^＋ or R^d described by a Gibbsian probability measure μη∧ associated with a pair interaction φ, the inverse temperature β, the activity z 〉 0, and the boundary condition η. Define F ∫ωf（s）wA（ds）. Applying the generalized Ito＇s formula for forward-backward martingales （see Klein et M. [5]）, we obtain convex concentration inequalities for F with respect to the Gibbs measure μη∧. On the other hand, by FKG inequality on the Poisson space, we also give a new simple argument for the stochastic domination for the Gibbs measure.     

马氏过程Lipschitz可加泛函的中

本文利用Kato分析扰动定理,通过验证C2-正则性条件,给出了关于马氏过程Lipschitz可加泛函的中偏差和中心极限定理．     

法国数学课程标准简介

高一: 统计 1.通过中心趋势(平均值,中位数,众数,截尾均值)和离散程度的一个或几个指标来概括.