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| - KPZ formula for log-infinitely divisible multifractal random measures
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| - We consider the continuous model of log-infinitely divisible multifractal random measures (MRM) introduced in [E. Bacry et al. Comm. Math. Phys.236 (2003) 449-475]. 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 dim H of a measurable set K and the Hausdorff dimension dim Hρ with respect to ρ of the same set: ζ(dim Hρ( K)) = dim H( K). Our results can be extended to all dimensions: inspired by quantum gravity in dimension 2, we focus on the log normal case in dimension 2.
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| - © EDP Sciences, SMAI, 2011
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