Bella, PeterSchäffner, Mathias2022-04-132022-04-132021-07-30http://hdl.handle.net/2003/40853http://dx.doi.org/10.17877/DE290R-22710We study local regularity properties of linear, non-uniformly parabolic finite-difference operators in divergence form related to the random conductance model on Zd. In particular, we provide an oscillation decay assuming only certain summability properties of the conductances and their inverse, thus improving recent results in that direction. As an application, we provide a local limit theorem for the random walk in a random degenerate and unbounded environment.enProcesses in random environmentsFunctional limit theoremsSmoothness and regularity of solutions to PDEsDegenerate parabolic equations510Text