Monotonicity for excited random walk in high dimensions

TL;DR

This paper proves that in high dimensions (d ≥ 9), the drift of excited random walk increases monotonically with the excitement parameter, providing insight into the behavior of such stochastic processes.

Contribution

It establishes the monotonicity of the drift in the excitement parameter for excited random walks in high dimensions, a result not previously known.

Findings

Drift is monotone in excitement parameter for d ≥ 9

Provides theoretical proof for high-dimensional excited random walks

Enhances understanding of stochastic process behavior in high dimensions

Abstract

We prove that the drift $\theta(d,\beta)$ for excited random walk in dimension $d$ is monotone in the excitement parameter $\beta \in[0, 1]$, when $d\ge 9$.