A note on the fragmentation of a stable tree

Philippe Marchal

doi:10.46298/dmtcs.3586

Philippe Marchal - A note on the fragmentation of a stable tree

dmtcs:3586 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science - https://doi.org/10.46298/dmtcs.3586

A note on the fragmentation of a stable treeConference paper

Authors: Philippe Marchal ^1,^2,³

1 Département de Mathématiques et Applications - ENS Paris [DMA]
2 Département de Mathématiques et Applications - ENS-PSL
3 Département de Mathématiques et Applications - ENS-PSL (UMR8553) [DMA]

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.

https://doi.org/10.46298/dmtcs.3586

Source: HAL:hal-01194672v1

Volume: DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science

Section: Proceedings

Published on: January 1, 2008

Imported on: May 10, 2017

Keywords: stable tree,fragmentation,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS],[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]

Bibliographic References

19 Documents citing this article

Nicholas Chee;Franz Rembart;Matthias Winkel, 2024, A recursive distributional equation for the stable tree, Bernoulli, 30, 2, 10.3150/23-bej1623, https://doi.org/10.3150/23-bej1623.

Frederik Sørensen, 2023, A down‐up chain with persistent labels on multifurcating trees, Random Structures and Algorithms, 64, 2, pp. 354-400, 10.1002/rsa.21185, https://doi.org/10.1002/rsa.21185.

Thierry E. Huillet, 2023, Occupancy Problems Related to the Generalized Stirling Numbers, Journal of Statistical Physics, 191, 1, 10.1007/s10955-023-03216-1.

Delphin Sénizergues, 2021, Geometry of weighted recursive and affine preferential attachment trees, Electronic Journal of Probability, 26, none, 10.1214/21-ejp640, https://doi.org/10.1214/21-ejp640.

Frédérique Bassino;Mathilde Bouvel;Valentin Féray;Lucas Gerin;Mickaël Maazoun;et al., 2020, Universal limits of substitution-closed permutation classes, arXiv (Cornell University), 22, 11, pp. 3565-3639, 10.4171/jems/993, http://arxiv.org/abs/1706.08333.

Bénédicte Haas, arXiv (Cornell University), Scaling Limits of Markov-Branching Trees and Applications, pp. 3-50, 2018, 10.1007/978-3-319-77643-9_1, https://arxiv.org/abs/1605.07873.

Franz Rembart;Matthias Winkel, 2018, Recursive construction of continuum random trees, The Annals of Probability, 46, 5, 10.1214/17-aop1237, https://doi.org/10.1214/17-aop1237.

Nathan Ross;Yuting Wen, 2018, Scaling limits for some random trees constructed inhomogeneously, Electronic Journal of Probability, 23, none, 10.1214/17-ejp101, https://doi.org/10.1214/17-ejp101.

Nicolas Broutin;Cécile Mailler, 2018, And/or trees: a local limit point of view, Pure (University of Bath), 10.1002/rsa.20758, https://purehost.bath.ac.uk/ws/files/155617317/andortrees.pdf.

Camille Pagnard, 2017, Local limits of Markov branching trees and their volume growth, Electronic Journal of Probability, 22, none, 10.1214/17-ejp96, https://doi.org/10.1214/17-ejp96.

Thomas Duquesne;Minmin Wang, 2017, Decomposition of Lévy trees along their diameter, 53, 2, 10.1214/15-aihp725, https://hal.archives-ouvertes.fr/hal-01132231.

Olivier Bodini;Julien David;Philippe Marchal, Random-Bit Optimal Uniform Sampling for Rooted Planar Trees with Given Sequence of Degrees and Applications, pp. 97-114, 2016, 10.1007/978-3-319-29221-2_9, https://hal.science/hal-00932993.

Bénédicte Haas;Robin Stephenson, 2015, Scaling limits of $k$ -ary growing trees, Annales de l Institut Henri Poincaré Probabilités et Statistiques, 51, 4, 10.1214/14-aihp622, https://doi.org/10.1214/14-aihp622.

Christina Goldschmidt;Bénédicte Haas, 2015, A line-breaking construction of the stable trees, Electronic Journal of Probability, 20, none, 10.1214/ejp.v20-3690, https://doi.org/10.1214/ejp.v20-3690.

Jim Pitman;Douglas Rizzolo;Matthias Winkel, 2014, Regenerative tree growth: structural results and convergence, Electronic Journal of Probability, 19, none, 10.1214/ejp.v19-3040, https://doi.org/10.1214/ejp.v19-3040.

Nicolas Curien;Bénédicte Haas, 2012, The stable trees are nested, Probability Theory and Related Fields, 157, 3-4, pp. 847-883, 10.1007/s00440-012-0472-x, https://doi.org/10.1007/s00440-012-0472-x.

Bo Chen;Daniel Ford;Matthias Winkel, 2009, A new family of Markov branching trees: the alpha-gamma model, Electronic Journal of Probability, 14, none, 10.1214/ejp.v14-616, https://doi.org/10.1214/ejp.v14-616.

Thomas Duquesne;Jean-Francois Le Gall, 2009, On the re-rooting invariance property of Lévy trees, Electronic Communications in Probability, 14, none, 10.1214/ecp.v14-1484, https://doi.org/10.1214/ecp.v14-1484.

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.

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