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arXiv · 1501.03963

A Spectral decomposition for the Bolthausen-Sznitman coalescent and the Kingman coalescent

Jonas Kukla·Helmut H. Pitters
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Abstract

We consider both the Bolthausen-Sznitman and the Kingman coalescent restricted to the partitions of $\{1, \ldots, n\}.$ Spectral decompositions of the corresponding generators are derived. As an application we obtain a formula for the Green's functions and a short derivation of the well-known formula for the transition probabilities of the Bolthausen-Sznitman coalescent.

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Jonas Kukla, Helmut H. Pitters. 2015-01-16. A Spectral decomposition for the Bolthausen-Sznitman coalescent and the Kingman coalescent. https://arxiv.org/abs/1501.03963

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