# Berry-Esseen bound and Local Limit Theorem for the coefficients of products of random matrices

@inproceedings{Dinh2021BerryEsseenBA, title={Berry-Esseen bound and Local Limit Theorem for the coefficients of products of random matrices}, author={T. C. Dinh and Lucas Kaufmann and Hao Wu}, year={2021} }

Let μ be a probability measure on GLd(R) and denote by Sn := gn · · · g1 the associated random matrix product, where gj are i.i.d. with law μ. Under the assumptions that μ 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/ √ n) and a general Local Limit Theorem for the coefficients of Sn.

## 6 Citations

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