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April 1997 The fluctuation result for the multiple point range of two-dimensional recurrent random walks
Yuji Hamana
Ann. Probab. 25(2): 598-639 (April 1997). DOI: 10.1214/aop/1024404413

Abstract

We study the fluctuation problem for the multiple point range of random walks in the two dimensional integer lattice with mean 0 and finite variance. The $p$-multiple point range means the number of distinct sites with multiplicity $p$ of random walk paths before time $n$. The suitably normalized multiple point range is proved to converge to a constant, which is independent of the multiplicity, multiple of the renormalized self-intersection local time of a planar Brownian motion.

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Yuji Hamana. "The fluctuation result for the multiple point range of two-dimensional recurrent random walks." Ann. Probab. 25 (2) 598 - 639, April 1997. https://doi.org/10.1214/aop/1024404413

Information

Published: April 1997
First available in Project Euclid: 18 June 2002

zbMATH: 0890.60066
MathSciNet: MR1434120
Digital Object Identifier: 10.1214/aop/1024404413

Subjects:
Primary: 60J15
Secondary: 60F05

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.25 • No. 2 • April 1997
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