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Random walk on the range of random walk

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Croydon, David A.. (2009) Random walk on the range of random walk. Journal of Statistical Physics, Vol.136 (No.2). pp. 349-372. ISSN 0022-4715

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Official URL: http://dx.doi.org/10.1007/s10955-009-9785-2

Abstract

We study the random walk X on the range of a simple random walk on ℤ d in dimensions d≥4. When d≥5 we establish quenched and annealed scaling limits for the process X, which show that the intersections of the original simple random walk path are essentially unimportant. For d=4 our results are less precise, but we are able to show that any scaling limit for X will require logarithmic corrections to the polynomial scaling factors seen in higher dimensions. Furthermore, we demonstrate that when d=4 similar logarithmic corrections are necessary in describing the asymptotic behavior of the return probability of X to the origin.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Random walks (Mathematics), Stochastic processes, Scaling (Social sciences), Logarithmic functions
Journal or Publication Title:	Journal of Statistical Physics
Publisher:	Springer New York LLC
ISSN:	0022-4715
Official Date:	July 2009
Volume:	Vol.136
Number:	No.2
Page Range:	pp. 349-372
Identification Number:	10.1007/s10955-009-9785-2
Status:	Peer Reviewed
Access rights to Published version:	Open Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/2264