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.
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