Unique P-relative equilibrium states exist for uniformly Hölder potentials on random Anosov systems with one-dimensional stable leaves and fibrewise mixing, and they enjoy quenched exponential decay of correlations.
Quenched decay of correlations for nonuniformly hyperbolic random maps with an ergodic driving system
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Thermodynamic formalism for hyperbolic random dynamical systems
Unique P-relative equilibrium states exist for uniformly Hölder potentials on random Anosov systems with one-dimensional stable leaves and fibrewise mixing, and they enjoy quenched exponential decay of correlations.