Monotonicity for excited random walk in high dimensions

Abstract

We prove that the drift θ(d, β) for excited random walk in dimension d is monotone in the excitement parameter β ∈ [0,1], when d is sufficiently large. We give an explicit criterion for monotonicity involving random walk Green's functions, and use rigorous numerical upper bounds provided by Hara (Private communication, 2007) to verify the criterion for d ≥ 9. © The Author(s) 2009.