Open Access
December 2017 Asymptotic Lyapunov exponents for large random matrices
Hoi H. Nguyen
Ann. Appl. Probab. 27(6): 3672-3705 (December 2017). DOI: 10.1214/17-AAP1293

Abstract

Suppose that A1,,AN are independent random matrices of size n whose entries are i.i.d. copies of a random variable ξ of mean zero and variance one. It is known from the late 1980s that when ξ is Gaussian then N1logANA1 converges to logn as N. We will establish similar results for more general matrices with explicit rate of convergence. Our method relies on a simple interplay between additive structures and growth of matrices.

Citation

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Hoi H. Nguyen. "Asymptotic Lyapunov exponents for large random matrices." Ann. Appl. Probab. 27 (6) 3672 - 3705, December 2017. https://doi.org/10.1214/17-AAP1293

Information

Received: 1 July 2016; Revised: 1 January 2017; Published: December 2017
First available in Project Euclid: 15 December 2017

zbMATH: 06848276
MathSciNet: MR3737935
Digital Object Identifier: 10.1214/17-AAP1293

Subjects:
Primary: 15A52 , 60B10

Keywords: large random matrices , Lyapunov exponents

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.27 • No. 6 • December 2017
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