Central Limit Theorem for the Excited Random Walk in dimension $d \geq 2$

TL;DR

This paper establishes a law of large numbers and a central limit theorem for excited random walks in all dimensions greater than or equal to two, extending understanding of their long-term behavior.

Contribution

It proves the law of large numbers and central limit theorem for excited random walks in all dimensions d ≥ 2, filling a gap in the theoretical understanding.

Findings

Law of large numbers proven for excited random walks

Central limit theorem established in all dimensions d ≥ 2

Extends previous results to higher dimensions

Abstract

We prove that a law of large numbers and a central limit theorem hold for the excited random walk model in every dimension $d \geq 2$.