Shuhei Shibata: Functional limit theorems for elephant random walks on general periodic structures

Описание: Abstract: Elephant Random Walk (ERW) is a non-Markovian stochastic process that retains complete memory of its past, making it a fundamental model for studying reinforcement in stochastic processes. In this talk, we extend the analysis of ERWs beyond the classical lattice $\mathbb{Z}^d$ to general periodic structures, including triangular and hexagonal lattices, and we establish functional limit theorems for ERW on them. 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. We also present the phenomenon of infinite collisions between two independent ERWs on the integer lattice $\mathbb{Z}$.