Random iteration of rational functions

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Focusing on ergodic theory, this book delves into holomorphic random dynamical systems on the Riemann sphere. It presents significant advancements, including two generalizations of Denker and Urbäski's 1991 theorem regarding the existence and uniqueness of equilibrium states for rational functions. These results pertain to Hölder continuous potential functions that meet a specific "pressure gap" condition, and they also extend a theorem established by Jonsson in 2000, contributing to the understanding of dynamical systems in complex analysis.