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.
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Document type :
Preprints, Working Papers, ...
2009
Domain :

https://hal.archives-ouvertes.fr/hal-00375053
Contributor : Julien Berestycki <>
Submitted on : Sunday, April 12, 2009 - 1:00:45 PM
Last modification on : Wednesday, October 12, 2016 - 1:03:51 AM

Identifiers

• 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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