Equilibrium states for random lattice models of hyperbolic type

We study the structural stability of random coupled map lattice models of hyperbolic type under certain metrics. Furthermore, by describing the thermodynamic formalism of the underlying random spin lattice system, we prove the existence of equilibrium states for equi-Hölder continuous random functions on lattice models under the conditions of random weak interaction and translation invariance and present some partial results on the uniqueness of equilibrium states.