KPZ formula for log-infinitely divisible multifractal random measures
Probability
2008-07-28 v2
Abstract
We consider the continuous model of log-infinitely divisible multifractal random measures (MRM) introduced in \cite{bacry} . If M is a non degenerate multifractal measure with associated metric and structure function , we show that we have the following relation between the (Euclidian) Hausdorff dimension of a measurable set K and the Hausdorff dimension with respect to \rho of the same set: . Our results can be extended to higher dimensions in the log normal case: inspired by quantum gravity in dime nsion 2, we consider the 2 dimensional case.
Cite
@article{arxiv.0807.1036,
title = {KPZ formula for log-infinitely divisible multifractal random measures},
author = {Rémi Rhodes and Vincent Vargas},
journal= {arXiv preprint arXiv:0807.1036},
year = {2008}
}
Comments
Revised version: added the two dimensional case