Jonas Kukla, Helmut H. Pitters
Published 2015-01-16Version 1
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.
Total internal and external lengths of the Bolthausen-Sznitman coalescent
Asymptotics of the allele frequency spectrum associated with the Bolthausen-Sznitman coalescent
Spectral decomposition of fractional operators and reflected stable semigroups
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