Invariance Principle for the one-dimensional dynamic Random Conductance Model under Moment Conditions

Abstract

Recent progress in the understanding of quenched invariance principles (QIP) for a continuous-time random walk on ${\mathbb{Z}}^d$ in an environment of dynamical random conductances is reviewed and extended to the $1$-dimensional case. The law of the conductances is assumed to be ergodic with respect to time-space shifts and satisfies certain integrability conditions.

15 pages, 1 figure; submitted to the Proceedings of the "RIMS Symposium on Stochastic Analysis on Large Scale Interacting Systems", October 2015, Kyoto, Japan

References in corpus (4)

• An almost sure invariance principle for random walks in a space-time random environment
• Random Walk in Dynamic Markovian Random Environment
• Quenched invariance principle for random walks with time-dependent ergodic degenerate weights
• Stability and instability of Gaussian heat kernel estimates for random walks among time-dependent conductances

Cited by in corpus (2)

• Limit theory for random walks in degenerate time-dependent random environments
• An invariance principle for one-dimensional random walks in degenerate dynamical random environments