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

2015/01/16 by Jonas Kukla, Kukla, Jonas, Helmut H. Pitters +1
Mathematics · Physics and Astronomy · #Quantum chaos and dynamical systems #Random Matrices and Applications #Spectral Theory in Mathematical Physics #math.PR #msc:60C05 #msc:60J28 #msc:92D25

paper · pdf · doi:10.48550/arxiv.1501.03963

arxiv created 2015/01/16 · arxiv updated 2015/01/19

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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