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2015 Almost exponential decay for the exit probability from slabs of ballistic RWRE
Enrique Guerra, Alejandro Ramirez
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Electron. J. Probab. 20: 1-17 (2015). DOI: 10.1214/EJP.v20-3655

Abstract

It is conjectured that in dimensions d ≥ 2 any random walk in an i.i.d. uniformly elliptic random environment (RWRE) which is directionally transient is ballistic. The ballisticity conditions for RWRE somehow interpolate between directional transience and ballisticity and have served to quantify the gap which would need to be proven in order to answer affirmatively this conjecture. Two important ballisticity conditions introduced by Sznitman in 2001 and 2002 are the so called conditions (T′) and (T): given a slab of width L orthogonal to l, condition (T′) in direction l is the requirement that the annealed exit probability of the walk through the side of the slab in the half-space ${x : x \cdot l < 0}$, decays faster than $e(−CL^\gamma)$ for all $\gamma\in (0, 1)$ and some constant C &gt; 0, while condition (T) in direction l is the requirement that the decay is exponential e(−CL). It is believed that (T′) implies (T). In this article we show that (T′) implies at least an almost (in a sense to be made precise) exponential decay.

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Enrique Guerra. Alejandro Ramirez. "Almost exponential decay for the exit probability from slabs of ballistic RWRE." Electron. J. Probab. 20 1 - 17, 2015. https://doi.org/10.1214/EJP.v20-3655

Information

Accepted: 5 March 2015; Published: 2015
First available in Project Euclid: 4 June 2016

zbMATH: 1328.60225
MathSciNet: MR3325093
Digital Object Identifier: 10.1214/EJP.v20-3655

Subjects:
Primary: 60K37
Secondary: 82D30

JOURNAL ARTICLE
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