Monotonicity for excited random walk in high dimensions |
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| Authors: | Remco van der Hofstad Mark Holmes |
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| Institution: | 1. Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600?MB, Eindhoven, The Netherlands
2. Department of Statistics, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand
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| Abstract: | We prove that the drift θ(d, β) for excited random walk in dimension d is monotone in the excitement parameter ${\beta \in 0,1]}$ , 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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