Probability theory
Berry–Esseen type bounds for the matrix coefficients and the spectral radius of the left random walk on GL d ()
Comptes Rendus. Mathématique, Volume 360 (2022) no. G5, pp. 475-482.

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

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 GL d (), en supposant l’existence d’un moment exponentiel ou polynomial.

Received:
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DOI: 10.5802/crmath.312
Classification: 60F05, 60B15, 60G50
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
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     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},
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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, Volume 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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