Random iteration of rational functions

📖 The goal of this book is to study the ergodic theory of holomorphic random dynamical systems on the Riemann sphere. Specifically, the main results are two generalizations of a theorem of Denker and Urbański ('91) concerning existence and uniqueness of equilibrium states of rational functions with respect to Hölder continuous potential functions satisfying a "pressure gap" condition. The main results also generalize a theorem of Jonsson ('00).