2016/11/07 by Franz Rembart, Rembart, Franz, Matthias Winkel +1 · 1 citation
Computer Science · #60J80 #Data Management and Algorithms #FOS: Mathematics #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1611.02333
openalex publication_date 2016/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We embed Duquesne and Le Gall's stable tree into a binary compact continuum random tree (CRT) in a way that solves an open problem posed by Goldschmidt and Haas. This CRT can be obtained by applying a recursive construction method of compact CRTs as presented in earlier work to a specific distribution of a random string of beads, i.e. a random interval equipped with a random discrete measure. We also express this CRT as a tree built by replacing all branch points of a stable tree by rescaled i.i.d. copies of a Ford CRT. Some of these developments are carried out in a space of infinity-marked metric spaces generalising Miermont's notion of a k-marked metric space.