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 tree

Authors: Philippe Marchal ¹

1 Département de Mathématiques et Applications - ENS Paris

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]

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Source : ScholeXplorer IsRelatedTo ARXIV 2010.07880 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.2010.07880 10.48550/arxiv.2010.07880 2010.07880 Invariance principle for fragmentation processes derived from conditioned stable Galton-Watson trees

12 Documents citing this article

Source : OpenCitations

Bodini, Olivier; David, Julien; Marchal, Philippe, 2016, Random-Bit Optimal Uniform Sampling For Rooted Planar Trees With Given Sequence Of Degrees And Applications, Algorithms And Discrete Applied Mathematics, pp. 97-114, 10.1007/978-3-319-29221-2_9.

Broutin, Nicolas; Mailler, CĂŠcile, 2018, And/or Trees: A Local Limit Point Of View, Random Structures And Algorithms, 53, 1, pp. 15-58, 10.1002/rsa.20758.

Chen, Bo; Ford, Daniel; Winkel, Matthias, 2009, A New Family Of Markov Branching Trees: The Alpha-Gamma Model, Electronic Journal Of Probability, 14, none, 10.1214/ejp.v14-616.

Curien, Nicolas; Haas, BĂŠnĂŠdicte, 2012, The Stable Trees Are Nested, Probability Theory And Related Fields, 157, 3-4, pp. 847-883, 10.1007/s00440-012-0472-x.

Duquesne, Thomas; Le Gall, Jean-Francois, 2009, On The Re-Rooting Invariance Property Of LĂŠvy Trees, Electronic Communications In Probability, 14, none, 10.1214/ecp.v14-1484.

Goldschmidt, Christina; Haas, BĂŠnĂŠdicte, 2015, A Line-Breaking Construction Of The Stable Trees, Electronic Journal Of Probability, 20, none, 10.1214/ejp.v20-3690.

Haas, Bénédicte; Stephenson, Robin, 2015, Scaling Limits Of $K$-Ary Growing Trees, Annales De l'Institut Henri Poincaré, Probabilités Et Statistiques, 51, 4, 10.1214/14-aihp622.

Haas, BĂŠnĂŠdicte, 2018, Scaling Limits Of Markov-Branching Trees And Applications, XII Symposium Of Probability And Stochastic Processes, pp. 3-50, 10.1007/978-3-319-77643-9_1.

Pagnard, Camille, 2017, Local Limits Of Markov Branching Trees And Their Volume Growth, Electronic Journal Of Probability, 22, none, 10.1214/17-ejp96.

Pitman, Jim; Rizzolo, Douglas; Winkel, Matthias, 2014, Regenerative Tree Growth: Structural Results And Convergence, Electronic Journal Of Probability, 19, none, 10.1214/ejp.v19-3040.

Rembart, Franz; Winkel, Matthias, 2018, Recursive Construction Of Continuum Random Trees, The Annals Of Probability, 46, 5, 10.1214/17-aop1237.

Ross, Nathan; Wen, Yuting, 2018, Scaling Limits For Some Random Trees Constructed Inhomogeneously, Electronic Journal Of Probability, 23, none, 10.1214/17-ejp101.

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