Self-interacting random walks
Probability
2012-03-16 v1
Abstract
Let be -dimensional probability measures in with mean 0. At each step we choose one of the measures based on the history of the process and take a step according to that measure. We give conditions for transience of such processes and also construct examples of recurrent processes of this type. In particular, in dimension 3 we give the complete picture: every walk generated by two measures is transient and there exists a recurrent walk generated by three measures.
Cite
@article{arxiv.1203.3459,
title = {Self-interacting random walks},
author = {Yuval Peres and Serguei Popov and Perla Sousi},
journal= {arXiv preprint arXiv:1203.3459},
year = {2012}
}