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

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Let(gn)n≥1 be a sequence of independent and identically distributed positive random d × d matrices and consider the matrix product Gn=gn… g1 Under suitable conditions,we establish the Berry-Esseen bounds on the rate of convergence in the central limit theorem and Cramér-type moderate deviation expansions,for any matrix norm ‖Gn‖ of Gn,its entries Gi,jn and its spectral radius ρ(Gn).Extended versions of their joint law with the direction of the random walk Gnx are also established,where x is a starting point in the unit sphere of Rd.

Berry-Esseen boundCramér-type moderate deviationproduct of random matricesoperator normentryspectral radius

Hui Xiao、Ion Grama、Quansheng Liu

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Institut für Mathematik und Angewandte Informatik,Universität Hildesheim,Hildesheim 31141,Germany

Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China

LMBA,Université Bretagne Sud,CNRS UMR 6205,Vannes F-56000,France

Deutsche Forschungsgemeinschaft(DFG)Centre Henri Lebesgue(CHL)国家自然科学基金国家自然科学基金国家自然科学基金国家自然科学基金

ME 4473/2-1ANR-11-LABX-0020-0111971063117310121227106212288201

2024

10.1007/s11425-021-2067-4

中国科学:数学(英文版)
中国科学院

中国科学:数学(英文版)

CSTPCD
影响因子：0.36
ISSN：1674-7283
年,卷(期)：2024.67(3)
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