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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

Dates:

Date	Event
July 2009	UNSPECIFIED

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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