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2015 A spectral decomposition for the Bolthausen-Sznitman coalescent and the Kingman coalescent
Jonas Kukla, Helmut Pitters
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Electron. Commun. Probab. 20: 1-13 (2015). DOI: 10.1214/ECP.v20-4612


We consider both the Bolthausen-Sznitman and the Kingman coalescent restricted to the partitions of <span id="MathJax-Element-1-Frame" class="MathJax"><span id="MathJax-Span-1" class="math"><span id="MathJax-Span-2" class=""><span id="MathJax-Span-3" class="mo">{<span id="MathJax-Span-4" class="mn">1<span id="MathJax-Span-5" class="mo">,<span id="MathJax-Span-6" class="mo">…<span id="MathJax-Span-7" class="mo">,<span id="MathJax-Span-8" class="mi">n<span id="MathJax-Span-9" class="mo">}<span id="MathJax-Span-10" class="mo">. 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 Pitters. "A spectral decomposition for the Bolthausen-Sznitman coalescent and the Kingman coalescent." Electron. Commun. Probab. 20 1 - 13, 2015.


Accepted: 20 November 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1333.60167
MathSciNet: MR3434204
Digital Object Identifier: 10.1214/ECP.v20-4612

Primary: 60J27
Secondary: 60C05 , 92D15

Keywords: Bolthausen-Sznitman coalescent , Green's matrix , Kingman coalescent , Random recursive tree , spectral decomposition

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