The multifractal structure of super-Brownian motion

Perkins, Edwin A and Taylor, S James (1998) The multifractal structure of super-Brownian motion. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 34 (1). pp. 97-138. ISSN 0246-0203

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We calculate the multifractal spectrum and mass exponents for super-Brownian motion in three or more dimensions. The former is trivial for points of unusually high density but not for points in the support of unusually low density. This difference is due to the presence of sets of points in the support (of positive dimension) about which there are asymptotically large empty annuli. This behaviour is quite different from that of ordinary Brownian motion and invalidates the multifractal formalism in the physics literature. The mass exponents for packing and Hausdorff measure are distinct, and both are piecewise linear.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: EPrints Services
Date Deposited: 06 Feb 2012 18:33
Last Modified: 02 Jun 2021 08:47
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