2005/03/31 by Christoph Richard · 1 citation
Computer Science · Mathematics · #Data Management and Algorithms #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #math.CO #math.PR #msc:05A15 #msc:39A13 #msc:60C05 #msc:82B41
paper · pdf · doi:10.1016/j.disc.2007.12.072
published as Discrete Mathematics 309 (2009) 207-230 · 35 pages, 1 figure. New introduction, typographical errors corrected
arxiv created 2007/09/24 · openalex publication_date 2008/03/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/02
We analyse q-functional equations arising from tree-like combinatorial structures, which are counted by size, internal path length, and certain generalisations thereof. The corresponding counting parameters are labelled by a positive integer k. We show the existence of a joint limit distribution for these parameters in the limit of infinite size, if the size generating function has a square root as dominant singularity. The limit distribution coincides with that of integrals of k-th powers of the standard Brownian excursion. Our approach yields a recursion for the moments of the limit distribution. It can be used to analyse asymptotic expansions of the moments, and it admits an extension to other types of singularity.