Open Access
December 2024 How often can two independent elephant random walks on $\mathbf{Z}$ meet?
Rahul Roy, Masato Takei, Hideki Tanemura
Proc. Japan Acad. Ser. A Math. Sci. 100(10): 57-59 (December 2024). DOI: 10.3792/pjaa.100.012

Abstract

We show that two independent elephant random walks on the integer lattice $\mathbf{Z}$ meet each other finitely often or infinitely often depends on whether the memory parameter $p$ is strictly larger than $3/4$ or not. Asymptotic results for the distance between them are also obtained.

Citation

Download Citation

Rahul Roy. Masato Takei. Hideki Tanemura. "How often can two independent elephant random walks on $\mathbf{Z}$ meet?." Proc. Japan Acad. Ser. A Math. Sci. 100 (10) 57 - 59, December 2024. https://doi.org/10.3792/pjaa.100.012

Information

Published: December 2024
First available in Project Euclid: 3 December 2024

Digital Object Identifier: 10.3792/pjaa.100.012

Subjects:
Primary: 60K35

Keywords: Elephant random walks , Random walks with memory , Self-interacting random walks

Rights: Copyright © 2024 The Japan Academy

Vol.100 • No. 10 • December 2024
Back to Top