Long range one-cookie random walk with positive speed
Probability
2021-10-07 v2
Abstract
We study one-dimensional excited random walks with non-nearest neighbor jumps. When the process is at a vertex that has not been visited before, its next transition has a positive drift to the right, possibly with long jumps. Whenever the process visits a vertex that has already been visited in the past, its next transition is the one of a simple symmetric random walk. We give a sufficient condition for the process to have positive speed.
Cite
@article{arxiv.2011.00493,
title = {Long range one-cookie random walk with positive speed},
author = {Andrea Collevecchio and Kais Hamza and Tuan-Minh Nguyen},
journal= {arXiv preprint arXiv:2011.00493},
year = {2021}
}
Comments
latest version, 18 pages, 2 figures