Berry-Esseen bounds and moderate deviations for the norm, entries and spectral radius of products of positive random matrices  

作　　者：Hui Xiao Ion Grama Quansheng Liu 

机构地区：[1]Institut fur Mathematik und Angewandte Informatik,Universitat Hildesheim,Hildesheim 31141,Germany [2]Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [3]LMBA,Universite Bretagne Sud,CNRS UMR 6205,Vannes F-56000,France

出　　处：《Science China Mathematics》2024年第3期627-646,共20页中国科学（数学）（英文版）

基　　金：supported by Deutsche Forschungsgemeinschaft (DFG) (Grant No. ME 4473/2-1);the Centre Henri Lebesgue (CHL) (Grant No. ANR-11-LABX-0020-01);National Natural Science Foundation of China (Grants Nos. 11971063, 11731012, 12271062 and 12288201)。

摘　　要：Let(g_(n))_(n≥1) be a sequence of independent and identically distributed positive random d×d matrices and consider the matrix product G_(n)=g_(n)…g_1.Under suitable conditions,we establish the Berry-Esseen bounds on the rate of convergence in the central limit theorem and Cramer-type moderate deviation expansions,for any matrix norm ‖G_(n)‖ of G_(n),its entries G_(n)^(i,j) and its spectral radius ρ(G_(n)).Extended versions of their joint law with the direction of the random walk G_(n)x are also established,where x is a starting point in the unit sphere of R~d.

关 键 词：Berry-Esseen bound Cramér-type moderate deviation product of random matrices operator norm ENTRY spectral radius 

分 类 号：O151.21[理学—数学]