Stuck Walks
Probability
2017-07-18 v1
Abstract
We investigate the asymptotic behaviour of a class of self-interacting nearest neighbour random walks on the one-dimensional integer lattice which are pushed by a particular linear combination of their own local time on edges in the neighbourhood of their current position. We prove that in a range of the relevant parameter of the model such random walkers can be eventually confined to a finite interval of length depending on the parameter value. The phenomenon arises as a result of competing self-attracting and self-repelling effects where in the named parameter range the former wins.
Cite
@article{arxiv.1011.1103,
title = {Stuck Walks},
author = {Anna Erschler and Balint Toth and Wendelin Werner},
journal= {arXiv preprint arXiv:1011.1103},
year = {2017}
}