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Pré-Publication, Document De Travail Année : 2008

KPZ formula for log-infinitely divisible multifractal random measures

Résumé

We consider the continuous model of log-infinitely divisible multifractal random measures (MRM) introduced in [1]. If M is a non degenerate multifractal measure with associated metric ρ(x, y) = M ([x, y]) and structure function ζ , we show that we have the following relation between the (Euclidian) Hausdorff dimension dimH of a mea- surable set K and the Hausdorff dimension dimρ H with respect to ρ of the same set: ζ (dimρ (K)) = dimH (K). Our results can be extended to higher dimensions in the log normal case: inspired by quantum gravity in dimension 2, we consider the 2 dimensional case.
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Dates et versions

hal-00293878 , version 1 (07-07-2008)
hal-00293878 , version 2 (27-07-2008)

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Rémi Rhodes, Vincent Vargas. KPZ formula for log-infinitely divisible multifractal random measures. 2008. ⟨hal-00293878v2⟩
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