On random walks and switched random walks on homogeneous spaces

Elvira Moreno, Mauricio Velasco

Abstract: We prove new mixing rate estimates for the random walks on homogeneous spaces determined by a probability distribution on a finite group . We introduce the switched random walk determined by a finite set of probability distributions on , prove that its long-term behaviour is determined by the Fourier joint spectral radius of the distributions, and give Hermitian sum-of-squares algorithms for the effective estimation of this quantity.