Work

A central limit theorem for unbalanced step-reinforced random walks

Year: 2025

Type: preprint

Abstract: In this paper, we study a class of unbalanced step-reinforced random walks that unifies the elephant random walk, the positively step-reinforced random walk, and the negatively step-reinforced random walk. By establishing a connection with bond percolation on random recursive trees, these processes can be represented as randomly weighted sums of independent and identically distributed random variables. We first derive normal and stable central limit theorems for such randomly weighted sums, and then apply these results to obtain a unified central limit theorem for unbalanced step-reinforced random walks.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2510.10898

Authors: Hu, Zhishui, Dong, Liang

Institutions: University of Science and Technology of China, Suzhou University of Technology

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4417100807

Cites:

Cited by:

Related to: