Abstract
We study random walks on the integers driven by a sample of time-dependent nearest-neighbor conductances that are bounded but are permitted to vanish over time intervals of positive Lebesgue-length. Assuming only ergodicity of the conductance law under space-time shifts and a moment assumption on the time to accumulate a unit conductance over a given edge, we prove that the walk scales, under a diffusive scaling of space and time, to a non-degenerate Brownian motion for a.e. realization of the environment. The conclusion particularly applies to random walks on one-dimensional dynamical percolation subject to fairly general stationary edge-flip dynamics.
Funding Statement
This work has been partially supported by NSF award DMS-1954343.
Acknowledgments
We thank an anonymous reviewer for helpful comments on the first version of this manuscript.
Citation
Marek Biskup. Minghao Pan. "An invariance principle for one-dimensional random walks in degenerate dynamical random environments." Electron. J. Probab. 28 1 - 18, 2023. https://doi.org/10.1214/23-EJP1053
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