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The multifractal structure of super-Brownian motion

journal contribution
posted on 2023-06-07, 20:29 authored by Edwin A Perkins, S James Taylor
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.

History

Publication status

  • Published

Journal

Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

ISSN

0246-0203

Publisher

Institute Henri Poincaré

Issue

1

Volume

34

Page range

97-138

ISBN

202347

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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