Random walks with unbounded jumps among random conductances II: Conditional quenched CLT

Abstract

We study a one-dimensional random walk among random conductances, with unbounded jumps. Assuming the ergodicity of the collection of conductances and a few other technical conditions (uniform ellipticity and polynomial bounds on the tails of the jumps) we prove a quenched conditional invariance principle for the random walk, under the condition that it remains positive until time $n$. As a corollary of this result, we study the effect of conditioning the random walk to exceed level $n$ before returning to 0 as $n\to \infty$.

23 pages. Final version of the second part of arXiv:1011.1196; to appear in ALEA

References in corpus (2)

• Invariance principles for random walks conditioned to stay positive
• Random walks with unbounded jumps among random conductances I: Uniform quenched CLT

Cited by in corpus (2)

• Random walks with unbounded jumps among random conductances I: Uniform quenched CLT
• Law of large numbers for random walk with unbounded jumps and BDP with bounded jumps in random environment