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Abstract
On the boundary of a Gallon Watson tree we can define the visibility measure by splitting mass equally between the children of each vertex, and the branching measure by splitting unit mass equally between all vertices in the nth generation and then letting n go to infinity. The multifractal structure of each of these measures is well studied. In this paper we address the question of a joint multifractal spectrum, i.e. we ask for the Hausdorff dimension of the boundary points which simultaneously have an unusual local dimension for both these measures. The resulting twoparameter spectrum exhibits a number of surprising new features, among them the emergence of a swallowtailshaped spectrum for the visibility measure in the presence of a nontrivial condition on the branching measure.
Original language  English 

Pages (fromto)  226245 
Number of pages  20 
Journal  Advances in Applied Probability 
Volume  42 
Issue number  1 
DOIs  
Publication status  Published  Mar 2010 
Keywords
 twodimensional multifractal analysis
 twoparameter spectrum
 branching process
 mixed spectrum
 percolation
 multifractal spectrum
 random tree
 selfsimilar fractal
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 1 Finished

INTERSECTION LOCAL TIMES AND STOCHASTIC PROCESSES IN RANDOM MEDIA
Morters, P.
Engineering and Physical Sciences Research Council
1/09/05 → 31/08/10
Project: Research council