An invariance principle for one-dimensional random walks among dynamical random conductances

Abstract

We study variable-speed random walks on $\mathbb{Z}$ driven by a family of nearest-neighbor time-dependent random conductances $\{a_t(x,x+1):x\in \mathbb{Z},t\ge 0\}$ whose law is assumed invariant and ergodic under space-time shifts. We prove a quenched invariance principle for the random walk under the minimal moment conditions on the environment; namely, assuming only that the conductances possess the first positive and negative moments. A novel ingredient is the representation of the parabolic coordinates and the corrector via a dual random walk which is considerably easier to analyze.

32 pages, 2 figs

References in corpus (2)

• Invariance principle for the random conductance model with unbounded conductances
• Limit theory for random walks in degenerate time-dependent random environments

Cited by in corpus (3)

• Symmetric simple exclusion process in dynamic environment: hydrodynamics
• An invariance principle for one-dimensional random walks in degenerate dynamical random environments
• Homogenization theory of random walks among deterministic conductances