Asymptotic Lyapunov exponents for large random matrices

Abstract

Suppose that A 1 , . . ., A N 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 N -1 log A N . . .A 1 converges to log √ n 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.

Locations

• arXiv (Cornell University) - View - PDF
• Project Euclid (Cornell University) - View - PDF
• The Annals of Applied Probability - View