A Liouville theorem for stationary and ergodic ensembles of parabolic systems

Abstract

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 $C^{1,\alpha }$-regularity estimate for caloric functions.

35 pages

References in corpus (2)

• An almost sure invariance principle for random walks in a space-time random environment
• Random Walk in Dynamic Markovian Random Environment