On the largest Lyapunov exponent for products of Gaussian matrices

Abstract

The paper provides a new integral formula for the largest Lyapunov exponent of Gaussian matrices, which is valid in the real, complex and quaternion-valued cases. This formula is applied to derive asymptotic expressions for the largest Lyapunov exponent when the size of the matrix is large and compare the Lyapunov exponents in models with a spike and no spikes.