Ergodicity index of the set of stochastic matrices

The paper introduces and explores the notions of ergodicity index and ergodicity exponent of a set of stochastic matrices. For the ergodicity exponent a sharp upper bound is obtained. A particular case of this bound is the well-known Paz bound. Also a connection between the ergodicity index and the Protasov–Voynov imprimitivity index is established.