On the measure division construction of Λ-coalescents

Abstract

This paper provides a new construction of Λ-coalescents called "measure division construction". This construction is pathwise and consists of dividing the characteristic measure Λinto several parts and adding them one by one to have a whole process. Using this construction, a "universal" normalization factor μ^{(n)} for the randomly chosen external branch length T^{(n)} has been discovered for a class of coalescents. This class of coalescents covers processes similar to Bolthausen-Sznitman coalescent, the coalescents without proper frequencies, and also others.

arXiv commentThe first version has a problem in the proof of Theorem 1.1 concerning the time back to MRCA and this theorem has been removed in the new version