A Liouville theorem for elliptic systems with degenerate ergodic coefficients

We study the behavior of second-order degenerate elliptic systems in divergence form with random coefficients which are stationary and ergodic. Assuming moment bounds like Chiarini and Deuschel (2014) on the coefficient field a and its inverse, we prove an intrinsic large-scale C1,α-regularity estimate for a-harmonic functions and obtain a first-order Liouville theorem for a-harmonic functions.