# KPZ formula for log-infinitely divisible multifractal random measures

ESAIM: Probability and Statistics (2012)

- Volume: 15, page 358-371
- ISSN: 1292-8100

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topRhodes, Rémi, and Vargas, Vincent. "KPZ formula for log-infinitely divisible multifractal random measures." ESAIM: Probability and Statistics 15 (2012): 358-371. <http://eudml.org/doc/222457>.

@article{Rhodes2012,

abstract = {
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 dimH of a measurable set K and the Hausdorff dimension dimHρ with respect to ρ of the same set: ζ(dimHρ(K)) = dimH(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.
},

author = {Rhodes, Rémi, Vargas, Vincent},

journal = {ESAIM: Probability and Statistics},

keywords = {Random measures; Hausdorff dimensions; multifractal processes; infinitely divisible random measure; Hausdorff dimension; Gaussian free field},

language = {eng},

month = {1},

pages = {358-371},

publisher = {EDP Sciences},

title = {KPZ formula for log-infinitely divisible multifractal random measures},

url = {http://eudml.org/doc/222457},

volume = {15},

year = {2012},

}

TY - JOUR

AU - Rhodes, Rémi

AU - Vargas, Vincent

TI - KPZ formula for log-infinitely divisible multifractal random measures

JO - ESAIM: Probability and Statistics

DA - 2012/1//

PB - EDP Sciences

VL - 15

SP - 358

EP - 371

AB -
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 dimH of a measurable set K and the Hausdorff dimension dimHρ with respect to ρ of the same set: ζ(dimHρ(K)) = dimH(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.

LA - eng

KW - Random measures; Hausdorff dimensions; multifractal processes; infinitely divisible random measure; Hausdorff dimension; Gaussian free field

UR - http://eudml.org/doc/222457

ER -

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