A Liouville theorem for stationary and ergodic ensembles of parabolic systems
Peter Bella, Alberto Chiarini, Benjamin Fehrman · Probability Theory and Related Fields · 2018
A first-order Liouville theorem is obtained for random ensembles of uniformly parabolic systems under the mere qualitative assumptions of stationarity and ergodicity. Furthermore, the paper establishes, almost surely, an intrinsic large-scale $$\mathcal {C}^{1,\alpha }$$ -regularity estimate for caloric functions.