Journal article
Monotonicity for excited random walk in high dimensions
R van der Hofstad, M Holmes
Probability Theory and Related Fields | SPRINGER HEIDELBERG | Published : 2010
Open access
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.
Grants
Funding Acknowledgements
The work of RvdH and MH was supported in part by Netherlands Organisation for Scientific Research (NWO). The work of MH was also supported by a FRDF grant from the University of Auckland. The authors thank Itai Benjamini for suggesting this problem to us, Takashi Hara for providing the Green's functions upper bounds in (5.4), and an anonymous referee for many helpful suggestions that significantly improved the presentation of this paper.