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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 TaylorWe 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.
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Publication status
- Published
Journal
Annales de l'Institut Henri Poincaré, Probabilités et StatistiquesISSN
0246-0203Publisher
Institute Henri PoincaréExternal DOI
Issue
1Volume
34Page range
97-138ISBN
202347Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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