A central limit theorem for random walk in random environment on marked Galton-Watson trees
Probability
2011-09-02 v6
Abstract
In this article we focus on a general model of random walk on random marked trees. We prove a recurrence criterion, analogue to the recurrence criterion proved by R. Lyons and Robin Pemantle (1992) in a slightly different model. In the critical case, we obtain a criterion for the positive/null recurrence. Several regimes appear, as proved (in a similar model), by Y. Hu and Z. Shi (2007). We focus on the "diffusive" regime and improve their result in this case, by obtaining a functional Central Limit Theorem. Our result is also an extension of a result by Y. Peres and O. Zeitouni (2008), obtained in the setting of biased random walk in Galton-Watson trees.
Cite
@article{arxiv.0812.1948,
title = {A central limit theorem for random walk in random environment on marked Galton-Watson trees},
author = {Gabriel Faraud},
journal= {arXiv preprint arXiv:0812.1948},
year = {2011}
}