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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 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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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: |
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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 (Creative Commons) |
Data sourced from Thomson Reuters' Web of Knowledge
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