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

作者：Kukla Jonas^*; Pitters Helmut H

来源：Electronic Communications in Probability, 2015, 20(0): 1-13.

DOI：10.1214/ECP.v20-4612

• Bolthausen-Sznitman coalescent
• Kingman coalescent
• spectral decomposition
• Green's matrix
• random recursive tree

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.

• 出版日期2015-11-20