Abstract
We study the asymptotic behaviour of random walks in i.i.d. non-elliptic random environments on $\mathbb{Z} ^d$. Standard conditions for ballisticity and the central limit theorem require ellipticity, and are typically non-local. We use oriented percolation and martingale arguments to find non-trivial local conditions for ballisticity and an annealed invariance principle in the non-elliptic setting. The use of percolation allows certain non-elliptic models to be treated even though ballisticity has not been proved for elliptic perturbations of these models.
Citation
Mark Holmes. Thomas S. Salisbury. "Conditions for ballisticity and invariance principle for random walk in non-elliptic random environment." Electron. J. Probab. 22 1 - 18, 2017. https://doi.org/10.1214/17-EJP107
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