Excited random walk in three dimensions has positive speed

TL;DR

This paper proves that in three dimensions, excited random walk exhibits a positive drift, meaning it moves to the right with non-zero speed, which advances understanding of its long-term behavior.

Contribution

It establishes that excited random walk in three dimensions has a positive speed, a significant result in understanding its asymptotic properties.

Findings

Excited random walk in 3D has positive speed.

The walk drifts to the right with non-zero velocity.

This confirms conjectures about the behavior of excited random walks in higher dimensions.

Abstract

Excited random walk is a random walk that has a positive drift to the right when it reaches a vertex it hasn't been to before. We show that in three dimensions the walk drifts to the right in non-zero speed.