The Annals of Probability
- Ann. Probab.
- Volume 25, Number 2 (1997), 598-639.
The fluctuation result for the multiple point range of two-dimensional recurrent random walks
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.
Ann. Probab., Volume 25, Number 2 (1997), 598-639.
First available in Project Euclid: 18 June 2002
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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