Abstract
We consider random walks in i.i.d. elliptic random environments which are not uniformly elliptic. We introduce a computable condition in dimension and a general condition valid for dimensions 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.
Funding Statement
Alejandro Ramírez and Rodrigo Ribeiro were supported by Iniciativa Científica Milenio of the Ministry of Science and Technology (Chile). Alejandro Ramírez has been also supported by Fondecyt 1220396.
Acknowledgments
The authors thank Daniel Kious for his valuable comments in the first version of this paper.
Citation
Alejandro F. Ramírez. Rodrigo Ribeiro. "Computable criteria for ballisticity of random walks in elliptic random environment." Electron. J. Probab. 27 1 - 38, 2022. https://doi.org/10.1214/22-EJP856
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