Step-reinforced random walks and one-half
Probability
2025-05-29 v2
Abstract
Under suitable moment assumptions, we show that a genuinely d-dimensional step-reinforced random walk undergoes a phase transition between recurrence and transience in dimensions , and that it is transient for all reinforcement parameters in dimensions , which solves a conjecture of Bertoin.
Cite
@article{arxiv.2402.16396,
title = {Step-reinforced random walks and one-half},
author = {Shuo Qin},
journal= {arXiv preprint arXiv:2402.16396},
year = {2025}
}
Comments
38 pages. This is the revised version of the previous paper Recurrence and Transience of Step-Reinforced Random Walks