KPZ formula for log-infinitely divisible multifractal random measures
| dc.creator | Rhodes, Rémi | |
| dc.creator | Vargas, Vincent | |
| dc.date | 2008-07-07 | |
| dc.date | 2008-07-27 | |
| dc.date.accessioned | 2026-07-07T09:52:47Z | |
| dc.date.available | 2026-07-07T09:52:47Z | |
| dc.description | 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 $ρ(x,y)=M([x,y])$ and structure function $\zet a$, we show that we have the following relation between the (Euclidian) Hausdorff dimension ${\rm dim}_H$ of a measurable set K and the Hausdorff dimension ${\rm dim}_H^ρ$ with respect to ρof the same set: $ζ({\rm dim}_H^ρ(K))={\r m dim}_H(K)$. 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. | |
| dc.description | Revised version: added the two dimensional case | |
| dc.identifier | https://arxiv.org/abs/0807.1036 | |
| dc.identifier | http://arxiv.org/abs/0807.1036 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165718 | |
| dc.subject | Probability | |
| dc.subject | 60G57, 28A78, 28A80 | |
| dc.title | KPZ formula for log-infinitely divisible multifractal random measures | |
| dc.type | text |