The multifractal spectrum of Brownian intersection local times

Details The multifractal spectrum of Brownian intersection local times The multifractal spectrum of Brownian intersection local times

2005-07-21

arxiv.org/abs/math/0507437v1

Annals of Probability 2005, Vol. 33, No. 4, 1255-1301

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117905000000116 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117905000000116

Let \ell be the projected intersection local time of two independent Brownian paths in R^d for d=2,3. We determine the lower tail of the random variable \ell(U), where 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.

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