Quenched and annealed equilibrium states for random Ruelle expanding maps and applications

In this paper we describe the spectral properties of semigroups expanding maps acting on Polish spaces, considering both sequences transfer operators along infinite compositions dynamics and integrated operators. We prove that there exists a limiting behaviour for such operators, these semigroup actions admit equilibrium states with exponential decay correlations several limit theorems. The reformulation results in terms quenched annealed extend by Baladi (1997) Carvalho, Rodrigues & Varandas (2017), where randomness is driven random walk phase space assumed to be compact. Furthermore, measures vary H\"older continuously can recovered from latter. Finally, give some applications context weighted non-autonomous iterated function systems, free boundary equilibria.