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BERRY-ESSEEN BOUND AND LOCAL LIMIT THEOREM FOR THE COEFFICIENTS OF PRODUCTS OF RANDOM MATRICES

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Title
BERRY-ESSEEN BOUND AND LOCAL LIMIT THEOREM FOR THE COEFFICIENTS OF PRODUCTS OF RANDOM MATRICES
Author(s)
Dinh, Tien-Cuong; Lucas Kaufmann; Wu, Hao
Publication Date
2024-03
Journal
Journal of the Institute of Mathematics of Jussieu, v.23, no.2, pp.705 - 735
Publisher
Cambridge University Press
Abstract
Let mu be a probability measure on GLd(R), and denote by Sn := gn middot middot middotg1 the associated random matrix product, where gj are i.i.d. with law mu. Under the assumptions that mu has a finite exponential moment and generates a proximal and strongly irreducible semigroup, we prove a Berry-Esseen bound with the optimal rate O(1/root n) for the coefficients of Sn, settling a long-standing question considered since the fundamental work of Guivarc'h and Raugi. The local limit theorem for the coefficients is also obtained, complementing a recent partial result of Grama, Quint and Xiao.
URI
https://pr.ibs.re.kr/handle/8788114/14960
DOI
10.1017/S1474748022000561
ISSN
1474-7480
Appears in Collections:
Center for Complex Geometry (복소기하학 연구단) > 1. Journal Papers (저널논문)
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