Elephant Random Walk on the Triangular Lattice

TL;DR

This paper extends the elephant random walk model to a triangular lattice in R^2, analyzing its behavior through scaling limits, and builds upon previous work to explore new geometric configurations.

Contribution

It introduces the elephant random walk on a triangular lattice, expanding the model's scope and analyzing its asymptotic behavior with new geometric considerations.

Findings

Derived scaling limits for the walk on the triangular lattice

Extended the model from previous studies to a new lattice structure

Provided insights into the walk's long-term behavior on complex geometries

Abstract

In this report, we introduce the elephant random walk on the triangular lattice over $R^2$ incorporating directions by extending the model developed in \cite{baur2016elephant}. We study the behavior of the walk by finding the appropriate scaling limits. This model was studied as a part of my Master of Statistics, 2018 final year dissertation at Indian Statistical Institute, Kolkata.