Dimension result and KPZ formula for two-dimensional multiplicative cascade processes

Abstract

We prove a Hausdorff dimension result for the image of two-dimensional multiplicative cascade processes, and we obtain from this result a KPZ-type formula which normally has one point of phase transition.

Published in at http://dx.doi.org/10.1214/10-AOP613 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (4)

• Log-infinitely divisible multifractal processes
• KPZ in one dimensional random geometry of multiplicative cascades
• Convergence of complex multiplicative cascades
• Another derivation of the geometrical KPZ relations