English

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 d=1,2d=1,2, and that it is transient for all reinforcement parameters in dimensions d3d\geq 3, which solves a conjecture of Bertoin.

Keywords

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

R2 v1 2026-06-28T14:59:57.993Z