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Conditions for ballisticity and invariance principle for random walk in non-elliptic random environment (1612.04761v1)
Published 14 Dec 2016 in math.PR
Abstract: We study the asymptotic behaviour of random walks in i.i.d. non-elliptic random environments on $\mathbb{Z}d$. Standard conditions (and proofs) for ballisticity and the central limit theorem require ellipticity. We use oriented percolation and martingale arguments to give non-trivial local conditions for ballisticity and an annealed invariance principle in the non-elliptic setting.