Central limit theorem for linear groups

DOI10.1214/15-AOP1002zbMath1341.22006OpenAlexW2963578987MaRDI QIDQ282514

Yves Benoist, Jean-François Quint

Publication date: 12 May 2016

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.aop/1457960397

zbMATH Keywords

martingalerandom walkstationary measurecocyclesemisimple group

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Sums of independent random variables; random walks (60G50) Discrete subgroups of Lie groups (22E40)

Related Items (41)

Joint spectrum and large deviation principle for random matrix products ⋮ Conditioned limit theorems for products of random matrices ⋮ Berry-Esseen bound and precise moderate deviations for products of random matrices ⋮ Berry-Esseen type bounds for the matrix coefficients and the spectral radius of the left random walk on \(\mathrm{GL}_d(\mathbb{R})\) ⋮ On the regularity of stationary measures ⋮ Deviation inequalities for random walks ⋮ Central limit theorems for mapping class groups and \(\operatorname{Out}(F_N)\) ⋮ A central limit theorem for the degree of a random product of Cremona transformations ⋮ Counting and boundary limit theorems for representations of Gromov‐hyperbolic groups ⋮ Berry-Esseen bounds with targets and local limit theorems for products of random matrices ⋮ Statistical distribution of the Stern sequence ⋮ Large deviation principle for random matrix products ⋮ Decay of Fourier coefficients for Furstenberg measures ⋮ Chaotic tracial dynamics ⋮ Large deviation expansions for the coefficients of random walks on the general linear group ⋮ Random walks on mapping class groups ⋮ Precise large deviation asymptotics for products of random matrices ⋮ 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 ⋮ Moderate deviations and local limit theorems for the coefficients of random walks on the general linear group ⋮ Limit theorems for the left random walk on \(\mathrm{GL}_{d}(\mathbb{R})\) ⋮ 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) ⋮ Random walks on hyperbolic spaces: second order expansion of the rate function at the drift ⋮ Central limit theorem for the entries of products of random matrices without the positivity condition ⋮ Rates of convergence in invariance principles for random walks on linear groups via martingale methods ⋮ The central limit theorem for eigenvalues ⋮ On the Komlós, Major and Tusnády strong approximation for some classes of random iterates ⋮ 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) ⋮ Lyapunov exponent and variance in the CLT for products of random matrices related to random Fibonacci sequences ⋮ Conditioned limit theorems for products of positive random matrices ⋮ Sharp connections between Berry-Esseen characteristics and Edgeworth expansions for stationary processes ⋮ Large deviations for random walks on free products of finitely generated groups ⋮ The joint spectrum ⋮ A zero-one law for invariant measures and a local limit theorem for coefficients of random walks on the general linear group ⋮ Random matrix products when the top Lyapunov exponent is simple ⋮ Higher order asymptotics for large deviations – Part I ⋮ Random walks on hyperbolic spaces: concentration inequalities and probabilistic Tits alternative ⋮ CLT with explicit variance for products of random singular matrices related to Hill’s equation

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