Conditions for ballisticity and invariance principle for random walk in non-elliptic random environment
Mark Holmes, Thomas S Salisbury
ELECTRONIC JOURNAL OF PROBABILITY | UNIV WASHINGTON, DEPT MATHEMATICS | Published : 2017
We study the asymptotic behaviour of random walks in i.i.d. non-elliptic random environments on ℤd. 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.
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Awarded by Australian Research Council
Holmes's research was supported in part by the Marsden Fund, administered by RSNZ, and by Future Fellowship FT160100166 from the Australian Research Council. Salisbury's research is supported in part by NSERC. The authors wish to thank the referee and editor for a careful examination of the paper, and several helpful suggestions.