Lyapunov exponents for products of complex Gaussian random matrices

Abstract

The exact value of the Lyapunov exponents for the random matrix product $P_N=A_N{A}_{N-1}...A_1$ with each $A_i={\Sigma }^{1/2}{G}_i^{\mathrm{c}}$, where $\Sigma$ is a fixed $d\times d$ positive definite matrix and $G_i^{\mathrm{c}}$ a $d\times d$ complex Gaussian matrix with entries standard complex normals, are calculated. Also obtained is an exact expression for the sum of the Lyapunov exponents in both the complex and real cases, and the Lyapunov exponents for diffusing complex matrices.

15 pages

References in corpus (2)

• Eigenvalues and Singular Values of Products of Rectangular Gaussian Random Matrices (The Extended Version)
• Products of random matrices and generalised quantum point scatterers

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