2015/08/02 by Paul Balança, Balança, Paul
Mathematics · #60G17 #60J55 #60J80 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G17 #msc:60J55 #msc:60J80
paper · pdf · doi:10.48550/arxiv.1508.00229
50 pages. Major overhaul of the paper, correcting Theorem 4 and adding the study of the mass measure spectrum
arxiv created 2015/10/25 · arxiv updated 2015/10/27
In this work, we investigate the spectrum of singularities of random stable trees with parameter γ∈(1,2). We consider for that purpose the scaling exponents derived from two natural measures on stable trees: the local time ℓa and the mass measure m, providing as well a purely geometrical interpretation of the latter exponent. We first characterise the uniform component of the multifractal spectrum which exists at every level a>0 of stable trees and corresponds to large masses with scaling index h∈[\tfrac1+γγ,\tfracγγ-1] for the mass measure (or equivalently h∈ [\tfrac1γ,\tfrac1γ-1] for the local time). In addition, we investigate the distribution of vertices appearing at random levels with exceptionally large masses of index h∈[0,\tfrac1+γγ). Finally, we discuss more precisely the order of the largest mass existing on any subset T(F) of a stable tree, characterising the former with the packing dimension of the set F.