Limit behavior of linearly edge-reinforced random walks on the half-line

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Hu, Zechun, Song, Renming, Wang, Li
Format: Preprint
Published: 2026
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866915746792079360
author Hu, Zechun
Song, Renming
Wang, Li
author_facet Hu, Zechun
Song, Renming
Wang, Li
contents Motivated by the article [M. Takei, Electron. J. Probab. 26 (2021), article no. 104], we study the limit behavior of linearly edge-reinforced random walks on the half-line $\mathbb{Z}_+$ with reinforcement parameter $δ>0$, and each edge $\{x,x+1\}$ has the initial weight $x^α\ln^βx$ for $x > 1$ and $1$ for $x = 0, 1$. The aim of this paper is to study the almost sure limit behavior of the walk in the recurrent regime, and extend the results of Takei mentioned above.
format Preprint
id arxiv_https___arxiv_org_abs_2601_15627
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Limit behavior of linearly edge-reinforced random walks on the half-line
Hu, Zechun
Song, Renming
Wang, Li
Probability
Motivated by the article [M. Takei, Electron. J. Probab. 26 (2021), article no. 104], we study the limit behavior of linearly edge-reinforced random walks on the half-line $\mathbb{Z}_+$ with reinforcement parameter $δ>0$, and each edge $\{x,x+1\}$ has the initial weight $x^α\ln^βx$ for $x > 1$ and $1$ for $x = 0, 1$. The aim of this paper is to study the almost sure limit behavior of the walk in the recurrent regime, and extend the results of Takei mentioned above.
title Limit behavior of linearly edge-reinforced random walks on the half-line
topic Probability
url https://arxiv.org/abs/2601.15627