Computable criteria for ballisticity of random walks in elliptic random environment

Alejandro F. Ramírez; Rodrigo Ribeiro

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arXiv · 2107.00113

Computable criteria for ballisticity of random walks in elliptic random environment

Alejandro F. Ramírez·Rodrigo Ribeiro

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Abstract

We consider random walks in i.i.d. elliptic random environments which are not uniformly elliptic. We introduce a computable condition in dimension $d=2$ and a general condition valid for dimensions $d\ge 2$ expressed in terms of the exit time from a box, which ensure that local trapping would not inhibit a ballistic behavior of the random walk. An important technical innovation related to our computable condition, is the introduction of a geometrical point of view to classify the way in which the random walk can become trapped, either in an edge, a wedge or a square. Furthermore, we prove that the general condition we introduce is sharp.

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BibTeX RIS

Alejandro F. Ramírez, Rodrigo Ribeiro. 2021-06-30. Computable criteria for ballisticity of random walks in elliptic random environment. https://arxiv.org/abs/2107.00113

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