Monotonicity for excited random walk 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 $d\ge 9$.

14 pages - changed references, typos

References in corpus (2)

• Excited random walk in three dimensions has positive speed
• Excited random walk in two dimensions has linear speed