Limit distribution of the quartet balance index for Aldous's b>=0-model

Abstract: This paper builds up on T. Martinez-Coronado, A. Mir, F. Rossello and G. Valiente's work "A balance index for phylogenetic trees based on quartets", introducing a new balance index for trees. We show here that this balance index, in the case of Aldous's b>=0-model, convergences weakly to a distribution that can be characterized as the fixed point of a contraction operator on a class of distributions.