Identification of the rate function for large deviations of an irreducible Markov chain.
A new criterion for the existence of an invariant distribution for Markov operators is presented. Moreover, it is also shown that the unique invariant distribution of an iterated function system is singular with respect to the Hausdorff measure.
Let be a measure on a domain in such that the Bergman space of holomorphic functions in possesses a reproducing kernel and . The Berezin transform associated to is the integral...