Let ℓ be the projected intersection local time of two independent Brownian paths in ℝd for d=2,3. We determine the lower tail of the random variable $\ell(\mathbb {U})$ , where $\mathbb {U}$ is the unit ball. The answer is given in terms of intersection exponents, which are explicitly known in the case of planar Brownian motion. We use this result to obtain the multifractal spectrum, or spectrum of thin points, for the intersection local times.
Publié le : 2005-07-14
Classification:
Brownian motion,
intersection of Brownian paths,
intersection local time,
Wiener sausage,
lower tail asymptotics,
intersection exponent,
Hausdorff measure,
thin points,
Hausdorff dimension spectrum,
multifractal spectrum,
60J65,
60G17,
60J55
@article{1120224581,
author = {Klenke, Achim and M\"orters, Peter},
title = {The multifractal spectrum of Brownian intersection local times},
journal = {Ann. Probab.},
volume = {33},
number = {1},
year = {2005},
pages = { 1255-1301},
language = {en},
url = {http://dml.mathdoc.fr/item/1120224581}
}
Klenke, Achim; Mörters, Peter. The multifractal spectrum of Brownian intersection local times. Ann. Probab., Tome 33 (2005) no. 1, pp. 1255-1301. http://gdmltest.u-ga.fr/item/1120224581/