We introduce a recursive algorithm generating random trees, which we identify as skeletons of a continuous, stable tree. We deduce a representation of a fragmentation process on these trees.
Thierry E. Huillet, 2023, Occupancy Problems Related to the Generalized Stirling Numbers, Journal of Statistical Physics, 191, 1, 10.1007/s10955-023-03216-1.
Bénédicte Haas;Grégory Miermont;Jim Pitman;Matthias Winkel, 2008, Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models, The Annals of Probability, 36, 5, 10.1214/07-aop377, https://doi.org/10.1214/07-aop377.