Berry–Esseen type bounds for the matrix coefficients and the spectral radius of the left random walk on $GL_d({\protect \mathbb{R}})$

Cuny, Christophe; Dedecker, Jérôme; Merlevède, Florence; Peligrad, Magda

doi:10.5802/crmath.312

Probabilités

Berry–Esseen type bounds for the matrix coefficients and the spectral radius of the left random walk on

G L_{d} (ℝ)

[Inégalités de type Berry–Esseen pour les coefficients matriciels et pour le rayon spectral de la marche aléatoire gauche sur

G L_{d} (ℝ)

]

Cuny, Christophe ¹ ; Dedecker, Jérôme ² ; Merlevède, Florence ³ ; Peligrad, Magda ⁴

¹ Univ. Brest, LMBA, UMR 6205 CNRS, 6 avenue Victor Le Gorgeu, 29238 Brest, France
² Université Paris Cité, MAP5, UMR 8145 CNRS, 45 rue des Saints-Pères, F-75006 Paris, France
³ Univ. Gustave Eiffel, Univ. Paris Est Créteil, UMR 8050 CNRS, LAMA, F-77454 Marne-la-Vallée, France
⁴ Department of Mathematical Sciences, University of Cincinnati, PO Box 210025, Cincinnati, Oh 45221-0025, USA

Comptes Rendus. Mathématique, Tome 360 (2022) no. G5, pp. 475-482.

Résumé
Abstract

Nous donnons des vitesses de convergence dans le théorème limite central pour les coefficients matriciels et pour le rayon spectral de la marche aléatoire gauche sur $G L_{d} (ℝ)$ , en supposant l’existence d’un moment exponentiel ou polynomial.

We give rates of convergence in the Central Limit Theorem for the matrix coefficients and the spectral radius of the left random walk on $G L_{d} (ℝ)$ , assuming the existence of an exponential or polynomial moment.

Reçu le : 2021-10-18
Révisé le : 2021-12-08
Accepté le : 2021-12-09
Publié le : 2022-05-23

DOI : 10.5802/crmath.312

Classification : 60F05, 60B15, 60G50

Affiliations des auteurs :

Cuny, Christophe ¹ ; Dedecker, Jérôme ² ; Merlevède, Florence ³ ; Peligrad, Magda ⁴

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     author = {Cuny, Christophe and Dedecker, J\'er\^ome and Merlev\`ede, Florence and Peligrad, Magda},
     title = {Berry{\textendash}Esseen type bounds for the matrix coefficients and the spectral radius of the left random walk on $GL_d({\protect \mathbb{R}})$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {475--482},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {360},
     number = {G5},
     year = {2022},
     doi = {10.5802/crmath.312},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/crmath.312/}
}

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Cuny, Christophe; Dedecker, Jérôme; Merlevède, Florence; Peligrad, Magda. Berry–Esseen type bounds for the matrix coefficients and the spectral radius of the left random walk on $GL_d({\protect \mathbb{R}})$. Comptes Rendus. Mathématique, Tome 360 (2022) no. G5, pp. 475-482. doi : 10.5802/crmath.312. http://www.numdam.org/articles/10.5802/crmath.312/

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