Monotonicity for excited random walk in high dimensions
成果类型：
Article
署名作者：
van der Hofstad, Remco; Holmes, Mark
署名单位：
Eindhoven University of Technology; University of Auckland
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-009-0215-9
发表日期：
2010
页码：
333-348
关键词：
摘要：
We prove that the drift theta(d, beta) for excited random walk in dimension d is monotone in the excitement parameter beta is an element of [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.
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