# Lyapunov exponents and random matrices

*by Prof Peter Forrester*

*Institution:*The University of Melbourne

*Date: Mon 17th September 2012*

*Time: 1:00 PM*

*Location: Room 115, Sidney Myer Asia Centre*

*Abstract*: Lyapunov exponents in random matrix theory relate to products of random matrices. I'll discuss how products of random matrices enters into some problems of mathematical and applied mathematics. Some comments will be make too about general methods to calculate Lyapunov exponents. My own contribution, which is the exact computation of Lyapunov exponents for the random matrix product \(P_N = A_N A_{N-1} \cdots A_1\), with each \(A_i = \Sigma^{1/2} G_i^{\rm c}\), where \(\Sigma\) is a fixed \(d \times d\) positive definite matrix and \(G_i^{\rm c}\) a \(d \times d\) complex Gaussian matrix with entries standard complex normals, will be outlined.