Dual random fragmentation and coagulation and an application to the genealogy of Yule processes. (English) Zbl 1064.60177

Bertoin, Jean; Goldschmidt, Christina

Drmota, Michael (ed.) et al., Mathematics and computer science III. Algorithms, trees, combinatorics and probabilities. Proceedings of the international colloquium of mathematics and computer sciences, Vienna, September 13–17, 2004. Basel: Birkhäuser (ISBN 3-7643-7128-5/hbk). Trends in Mathematics, 295-308 (2004).

In the first part the authors show that coagulation and fragmentation are inverse phenomena when Dirichlet and Poisson-Dirichlet processes are involved in a convenient way. They show in the second part that their dual fragmentation and coagulation chains are naturally connected to the genealogy of Yule processes after time-changing. They also consider the case of a continuous state Yule process.
For the entire collection see [Zbl 1047.68003].

Reviewer: Dominique Lepingle (Orléans)

MSC:

60J80

Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords:

random fragmentation; random coagulation; genealogical process; Yule process