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

DOI10.1214/ECP.V20-4612zbMATH Open1333.60167arXiv1501.03963OpenAlexW1570263368MaRDI QIDQ894516

Helmut Pitters, Jonas Kukla

Publication date: 1 December 2015

Published in: Electronic Communications in Probability (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1501.03963

zbMATH Keywords

spectral decompositionGreen's matrixrandom recursive treeBolthausen-Sznitman coalescentKingman coalescent

Mathematics Subject Classification ID

Problems related to evolution (92D15) Combinatorial probability (60C05) Continuous-time Markov processes on discrete state spaces (60J27) Applications of continuous-time Markov processes on discrete state spaces (60J28)

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