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Table of contents
1 Introduction
1.1 Objets étudiés
1.2 Aperçu des résultats
2 Ordered additive coalescent and Lévy processes
2.1 Introduction
2.2 Ordered additive coalescent
2.3 The Lévy fragmentation
2.4 The fragmentation semigroup
2.5 The left-most fragment
2.6 The mixing of extremal additive coalescents
2.7 Proof of Vervaat’s Theorem
2.8 Concluding remarks
3 Fragmentations and stable subordinators
3.1 Introduction
3.2 A Poisson process construction of self-similar fragmentations
3.3 Stable subordinators
3.4 Small-time behavior of self-similar fragmentations
3.5 Large-time behavior of self-similar fragmentations
3.6 One-dimensional distributions
3.7 Mass of a tagged fragment
4 Self-similar fragmentations of the stable tree I
4.1 Introduction
4.2 Preliminaries
4.3 Study of F−
4.4 Small-time asymptotics
4.5 On continuous-state branching processes…
5 Self-similar fragmentations of the stable tree II
5.1 Introduction
5.2 Some facts about Lévy processes
5.3 The stable tree
5.4 Study of F+
5.5 Study of F♮
5.6 Asymptotics
6 The genealogy of self-similar fragmentations
6.1 Introduction
6.2 The CRT TF
6.3 Hausdorff dimension of TF
7 The exploration process of the ICRT
7.1 Introduction
7.2 Constructing Xθ and Y θ
7.3 p-trees and associated processes
7.4 Convergence of p-trees to the ICRT
7.5 Height profile
7.6 The exploration process
7.7 Miscellaneous comments
8 Asymptotics for Random p-mappings
8.1 Introduction
8.2 Background
8.3 Proof of Theorem 8.1
8.4 Final comments
Bibliographie
