Asymptotic directions in random walks in random environment revisited

Alexander Drewitz; Alejandro F. Ramírez

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arXiv · 0902.1115

Asymptotic directions in random walks in random environment revisited

Alexander Drewitz·Alejandro F. Ramírez

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Abstract

Recently Simenhaus proved that for any elliptic random walk in random environment, transience in the neighborhood of a given direction is equivalent to the a.s. existence of a deterministic asymptotic direction and to transience in any direction in the open half space defined by this asymptotic direction. Here we prove an improved version of this result and review some open problems.

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Alexander Drewitz, Alejandro F. Ramírez. 2009-02-06. Asymptotic directions in random walks in random environment revisited. https://arxiv.org/abs/0902.1115

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