## The Annals of Applied Probability

### Asymptotic Lyapunov exponents for large random matrices

Hoi H. Nguyen

#### Abstract

Suppose that $A_{1},\dots ,A_{N}$ are independent random matrices of size $n$ whose entries are i.i.d. copies of a random variable $\xi$ of mean zero and variance one. It is known from the late 1980s that when $\xi$ is Gaussian then $N^{-1}\log \Vert A_{N}\dots A_{1}\Vert$ converges to $\log \sqrt{n}$ as $N\to \infty$. 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.

#### Article information

Source
Ann. Appl. Probab., Volume 27, Number 6 (2017), 3672-3705.

Dates
Revised: January 2017
First available in Project Euclid: 15 December 2017

https://projecteuclid.org/euclid.aoap/1513328711

Digital Object Identifier
doi:10.1214/17-AAP1293

Mathematical Reviews number (MathSciNet)
MR3737935

Zentralblatt MATH identifier
06848276

Subjects
Primary: 15A52 60B10: Convergence of probability measures

#### Citation

Nguyen, Hoi H. Asymptotic Lyapunov exponents for large random matrices. Ann. Appl. Probab. 27 (2017), no. 6, 3672--3705. doi:10.1214/17-AAP1293. https://projecteuclid.org/euclid.aoap/1513328711

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