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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. doi:10.1007/s10955-009-9785-2

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

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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
Dates:
DateEvent
July 2009UNSPECIFIED
Volume: Vol.136
Number: No.2
Page Range: pp. 349-372
DOI: 10.1007/s10955-009-9785-2
Status: Peer Reviewed
Access rights to Published version: Open Access

Data sourced from Thomson Reuters' Web of Knowledge

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