Asymptotic results on the length of coalescent trees

2007/06/01 by Jean-François Delmas, Jean‐François Delmas, Delmas, Jean-François +6
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #05C05 #60F05 #60G52 #60J70 #Bayesian Methods and Mixture Models #Evolution and Genetic Dynamics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:05C05 #msc:60F05 #msc:60G52 #msc:60J70

paper · pdf · doi:10.48550/arxiv.0706.0204

arxiv created 2007/06/01 · openalex publication_date 2007/06/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give the asymptotic distribution of the length of partial coalescent trees for Beta and related coalescents. This allows us to give the asymptotic distribution of the number of (neutral) mutations in the partial tree. This is a first step to study the asymptotic distribution of a natural estimator of DNA mutation rate for species with large families.

Citations

• On a random recursion related to absorption times of death Markov chains

Related

• Asympotic behavior of the total length of external branches for Beta-coalescents
• The minimal observable clade size of exchangeable coalescents
• The allelic partition for coalescent point processes
• Asymptotic sampling formulae for Lambda-coalescents
• Asymptotics of the allele frequency spectrum associated with the Bolthausen-Sznitman coalescent