Equilibrium states for random non-uniformly expanding maps

We show that for a robust ( C 2 -open) class of random non-uniformly expanding maps there exist equilibrium states for a large class of potentials. In particular, these sytems have measures of maximal entropy. These results also give a partial answer to a question posed by Liu–Zhao. The proof of the main result uses an extension of techniques in recent works by Alves–Araújo, Alves–Bonatti–Viana and Oliveira.