Basic properties of critical lognormal multiplicative chaos
Probability
2015-10-28 v4 Mathematical Physics
math.MP
Abstract
We study one-dimensional exact scaling lognormal multiplicative chaos measures at criticality. Our main results are the determination of the exact asymptotics of the right tail of the distribution of the total mass of the measure, and an almost sure upper bound for the modulus of continuity of the cumulative distribution function of the measure. We also find an almost sure lower bound for the increments of the measure almost everywhere with respect to the measure itself, strong enough to show that the measure is supported on a set of Hausdorff dimension .
Keywords
Cite
@article{arxiv.1303.4548,
title = {Basic properties of critical lognormal multiplicative chaos},
author = {Julien Barral and Antti Kupiainen and Miika Nikula and Eero Saksman and Christian Webb},
journal= {arXiv preprint arXiv:1303.4548},
year = {2015}
}
Comments
Published at http://dx.doi.org/10.1214/14-AOP931 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)