The Annals of Probability

The fluctuation result for the multiple point range of two-dimensional recurrent random walks

Yuji Hamana

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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.

Article information

Source
Ann. Probab., Volume 25, Number 2 (1997), 598-639.

Dates
First available in Project Euclid: 18 June 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1024404413

Digital Object Identifier
doi:10.1214/aop/1024404413

Mathematical Reviews number (MathSciNet)
MR1434120

Zentralblatt MATH identifier
0890.60066

Subjects
Primary: 60J15
Secondary: 60F05: Central limit and other weak theorems

Keywords
Multiple point range random walk intersection local time

Citation

Hamana, Yuji. The fluctuation result for the multiple point range of two-dimensional recurrent random walks. Ann. Probab. 25 (1997), no. 2, 598--639. doi:10.1214/aop/1024404413. https://projecteuclid.org/euclid.aop/1024404413


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