English

On the measure division construction of \Lambda-coalescents

Probability 2013-06-28 v3

Abstract

This paper provides a new construction of \Lambda-coalescents called "measure division construction". This construction is pathwise and consists of dividing the characteristic measure \Lambda into several parts and adding them one by one to have a whole process. Using this construction, a "universal" normalization factor \mu^{(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.

Keywords

Cite

@article{arxiv.1302.1083,
  title  = {On the measure division construction of \Lambda-coalescents},
  author = {Linglong Yuan},
  journal= {arXiv preprint arXiv:1302.1083},
  year   = {2013}
}

Comments

The 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

R2 v1 2026-06-21T23:21:10.595Z