# Kingman's coalescent and Brownian motion

Abstract : We describe a simple construction of Kingman's coalescent in terms of a Brownian excursion. This construction is closely related to, and sheds some new light on, earlier work by Aldous and Warren. Our approach also yields some new results: for instance, we obtain the full multifractal spectrum of Kingman's coalescent. This complements earlier work on Beta-coalescents by the authors and Schweinsberg. Surprisingly, the thick part of the spectrum is not obtained by taking the limit as $\alpha \to 2$ in the result for Beta-coalescents mentioned above. Other analogies and differences between the case of Beta-coalescents and Kingman's coalescent are discussed.
Keywords :
Type de document :
Pré-publication, Document de travail
2009
Domaine :

https://hal.archives-ouvertes.fr/hal-00375053
Contributeur : Julien Berestycki <>
Soumis le : dimanche 12 avril 2009 - 13:00:45
Dernière modification le : mercredi 12 octobre 2016 - 01:03:51

### Identifiants

• HAL Id : hal-00375053, version 1
• ARXIV : 0904.1526

### Citation

J. Berestycki, N. Berestycki. Kingman's coalescent and Brownian motion. 2009. <hal-00375053>

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