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On the multifractal spectrum of the branching measure on a Galton–Watson tree

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Peter Mörters  and
Narn-Rueih Shieh
Peter Mörters*
Affiliation:
University of Bath
Narn-Rueih Shieh*
Affiliation:
National Taiwan University and NCTS, Taipei
*
∗ Postal address: Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK. Email address: [email protected]
∗∗ Postal address: Department of Mathematics, National Taiwan University, Taipei, Taiwan. Email address: [email protected]
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Abstract

Suppose that μ is the branching measure on the boundary of a supercritical Galton–Watson tree with offspring distribution N such that E[N log N] < ∞ and P{N = 1} > 0. We determine the multifractal spectrum of μ using a method different from that proposed by Shieh and Taylor, which is flawed.

Keywords

Galton–Watson treebranching measurebranching setpercolationHausdorff dimensiondimension spectrummultifractal spectrum

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60G17: Sample path properties
Type
Short Communications
Information
Journal of Applied Probability , Volume 41 , Issue 4 , December 2004 , pp. 1223 - 1229
Copyright
Copyright © Applied Probability Trust 2004 

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