Monotonicity for excited random walk in high dimensions

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We prove that the drift ¿(d, ß) for excited random walk in dimension d is monotone in the excitement parameter ß [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.
Original languageEnglish
Pages (from-to)333-348
JournalProbability Theory and Related Fields
Issue number1-2
Publication statusPublished - 2010


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