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arXiv · 2511.10347

Functional limit theorems for elephant random walks on general periodic structures

Shuhei Shibata
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Abstract

This paper investigates functional limit theorems for the Elephant Random Walk (ERW) on general periodic structures, extending the Bertenghi's results on $\mathbb{Z}^d$. Our results reveal new structure-dependent quantities that do not appear in the classical setting $\mathbb{Z}^d$, highlighting how the underlying structure affects the asymptotic behavior of the walk.

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Shuhei Shibata. 2025-11-13. Functional limit theorems for elephant random walks on general periodic structures. https://arxiv.org/abs/2511.10347

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