English

Reinforced random walks under memory lapses

Probability 2021-09-22 v1 Mathematical Physics math.MP

Abstract

We introduce a one-dimensional random walk, which at each step performs a reinforced dynamics with probability θ\theta and with probability 1θ1 - \theta, the random walk performs a step independent of the past. We analyse its asymptotic behaviour, showing a law of large numbers and characterizing the diffusive and superdiffusive regions. We prove central limit theorems and law of iterated logarithm based on the martingale approach.

Keywords

Cite

@article{arxiv.2109.10301,
  title  = {Reinforced random walks under memory lapses},
  author = {Manuel González-Navarrete and Ranghely Hernández},
  journal= {arXiv preprint arXiv:2109.10301},
  year   = {2021}
}
R2 v1 2026-06-24T06:11:30.507Z