KPZ formula for log-infinitely divisible multifractal random measures

dc.creatorRhodes, Rémi
dc.creatorVargas, Vincent
dc.date2008-07-07
dc.date2008-07-27
dc.date.accessioned2026-07-07T09:52:47Z
dc.date.available2026-07-07T09:52:47Z
dc.descriptionWe 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.descriptionRevised version: added the two dimensional case
dc.identifierhttps://arxiv.org/abs/0807.1036
dc.identifierhttp://arxiv.org/abs/0807.1036
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/165718
dc.subjectProbability
dc.subject60G57, 28A78, 28A80
dc.titleKPZ formula for log-infinitely divisible multifractal random measures
dc.typetext

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