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| HAL: hal-00293878, version 2 |
| arXiv: 0807.1036 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2008-07-07) | v2 (2008-07-27) |
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| KPZ formula for log-infinitely divisible multifractal random measures |
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| Rémi Rhodes 1Vincent Vargas 1 |
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| (2008-07-07) |
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| 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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| 1: | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) |
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CNRS : UMR7534 – Université Paris IX - Paris Dauphine |
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| Subject | : | Mathematics/Probability |
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| Random measures – Hausdorff dimensions – Multifractal processes. |
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| hal-00293878, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00293878 | |
| oai:hal.archives-ouvertes.fr:hal-00293878 | |
| From: Vincent Vargas | |
| Submitted on: Sunday, 27 July 2008 16:14:54 | |
| Updated on: Sunday, 27 July 2008 20:51:15 | |
