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.
Publié le : 1997-04-14
Classification:
Multiple point range,
random walk,
intersection local time,
60J15,
60F05
@article{1024404413,
author = {Hamana, Yuji},
title = {The fluctuation result for the multiple point range of
two-dimensional recurrent random walks},
journal = {Ann. Probab.},
volume = {25},
number = {4},
year = {1997},
pages = { 598-639},
language = {en},
url = {http://dml.mathdoc.fr/item/1024404413}
}
Hamana, Yuji. The fluctuation result for the multiple point range of
two-dimensional recurrent random walks. Ann. Probab., Tome 25 (1997) no. 4, pp. 598-639. http://gdmltest.u-ga.fr/item/1024404413/