A binary embedding of the stable line-breaking construction

Franz Rembart and Matthias Winkel

Stochastic Processes and their Applications, 2023, vol. 163, issue C, 424-472

Abstract: 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 i.i.d. copies of a Ford CRT, each rescaled by a factor intrinsic to the stable CRT.

Keywords: Stable tree; Line-breaking construction; String of beads; Continuum random tree; Marked metric space; Recursive distribution equation (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2023.06.007

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