On estimating the derivatives of symmetric diffusions in stationary random environment, with applications to ∇φ interface model

Abstract

We consider diffusions on ℝ d or random walks on ℤ d in a random environment which is stationary in space and in time and with symmetric and uniformly elliptic coefficients. We show existence and Hölder continuity of second space derivatives and time derivatives for the annealed kernels of such diffusions and give estimates for these derivatives. In the case of random walks, these estimates are applied to the Ginzburg-Landau ∇φ interface model. © Springer-Verlag 2005.