Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896766 | Journal of Functional Analysis | 2018 | 62 Pages |
Abstract
We study continuous-time (variable speed) random walks in random environments on Zd, dâ¥2, where, at time t, the walk at x jumps across edge (x,y) at time-dependent rate at(x,y). The rates, which we assume stationary and ergodic with respect to space-time shifts, are symmetric and bounded but possibly degenerate in the sense that the total jump rate from a vertex may vanish over finite intervals of time. We formulate conditions on the environment under which the law of diffusively-scaled random walk path tends to Brownian motion for almost every sample of the rates. The proofs invoke Moser iteration to prove sublinearity of the corrector in pointwise sense; a key additional input is a conversion of certain weighted energy norms to ordinary ones. Our conclusions apply to random walks on dynamical bond percolation and interacting particle systems as well as to random walks arising from the Helffer-Sjöstrand representation of gradient models with certain non-strictly convex potentials.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Marek Biskup, Pierre-François Rodriguez,