Limit theorems for the left random walk on \(\mathrm{GL}_{d}(\mathbb{R})\)

DOI10.1214/16-AIHP773zbMath1388.60017arXiv1603.02217OpenAlexW2769645439MaRDI QIDQ1700394

Christophe Jan, Christophe Cuny, Jérôme Dedecker

Publication date: 5 March 2018

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.02217

zbMATH Keywords

central limit theoremstrong invariance principlesrandom walks on \(\mathrm{GL}_{d}(\mathbb{R})\)

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Functional limit theorems; invariance principles (60F17) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items (13)

Berry-Esseen type bounds for the matrix coefficients and the spectral radius of the left random walk on \(\mathrm{GL}_d(\mathbb{R})\) ⋮ Counting and boundary limit theorems for representations of Gromov‐hyperbolic groups ⋮ Large deviation expansions for the coefficients of random walks on the general linear group ⋮ Random walks on \(\mathrm{SL}_2({\mathbb{C}})\): spectral gap and limit theorems ⋮ Berry-Esseen type bounds for the left random walk on \({\mathrm{GL}_d}(\mathbb{R})\) under polynomial moment conditions ⋮ BERRY–ESSEEN BOUND AND LOCAL LIMIT THEOREM FOR THE COEFFICIENTS OF PRODUCTS OF RANDOM MATRICES ⋮ A Berry-Esseen bound with (almost) sharp dependence conditions ⋮ Geometric methods of complex analysis. Abstracts from the workshop held May 16--22, 2021 (hybrid meeting) ⋮ Rates of convergence in invariance principles for random walks on linear groups via martingale methods ⋮ Equidistribution of random walks on compact groups. II: The Wasserstein metric ⋮ Berry-Esseen bounds and moderate deviations for random walks on \(\mathrm{GL}_d(\mathbb{R})\) ⋮ Large and moderate deviations for the left random walk on GL d (R) ⋮ Sharp connections between Berry-Esseen characteristics and Edgeworth expansions for stationary processes

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