Expansiveness, specification, and equilibrium states for random bundle transformations

We introduce notions of expansiveness, conjugation, and specification for random bundle transformations and derive the uniqueness of equilibrium states for a large class of functions.We consider both invertible and noninvertible cases and discuss the results in the random subshifts case.As an example of such systems we introduce randomsofic shifts which can be described both via random graphs and as factors of random subshifts of finite type.Based on the random graph description we discuss large deviation results for random sofic shifts.