On the largest Lyapunov exponent for products of Gaussian random matrices

The paper provides a new 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. In addition, the pa-per gives new exact formulas for the largest Lyapunov exponents of 3-by-3 real and d-by-d quaternion Gaussian matrices. 1