Excited random walk against a wall
Probability
2007-05-23 v3
Abstract
We analyze random walk in the upper half of a three dimensional lattice which goes down whenever it encounters a new vertex, a.k.a. excited random walk. We show that it is recurrent with an expected number of returns of square-root log n.
Cite
@article{arxiv.math/0509464,
title = {Excited random walk against a wall},
author = {Gideon Amir and Itai Benjamini and Gady Kozma},
journal= {arXiv preprint arXiv:math/0509464},
year = {2007}
}
Comments
16 pages. Revised as per referee remarks. To appear in Probab. Theory Related Fields