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Article Dans Une Revue Annals of Probability Année : 2023

Berry-Esseen type bounds for the Left Random Walk on GL d (R) under polynomial moment conditions

Résumé

Let A n = ε_n • • • ε_1 , where (ε n) n≥1 is a sequence of independent random matrices taking values in GL d (R), d ≥ 2, with common distribution µ. In this paper, under standard assumptions on µ (strong irreducibility and proximality), we prove Berry-Esseen type theorems for log(||A n||) when µ has a polynomial moment. More precisely, we get the rate √ log n/ √ n when µ has a moment of order 3 and the rate 1/ √ n when µ has a moment of order 4, which significantly improves earlier results in this setting.
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Dates et versions

hal-03329189 , version 1 (30-08-2021)
hal-03329189 , version 2 (30-10-2022)

Identifiants

Citer

C. Cuny, J. Dedecker, F. Merlevède, M. Peligrad. Berry-Esseen type bounds for the Left Random Walk on GL d (R) under polynomial moment conditions. Annals of Probability, 2023, ⟨10.1214/22-AOP1602⟩. ⟨hal-03329189v2⟩
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