A Spectral decomposition for the Bolthausen-Sznitman coalescent and the Kingman coalescent
Abstract
We consider both the Bolthausen-Sznitman and the Kingman coalescent restricted to the partitions of \1, …, 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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