Recent progress in coalescent theory
N Berestycki - arXiv preprint arXiv:0909.3985, 2009 - arxiv.org
Coalescent theory is the study of random processes where particles may join each other to
form clusters as time evolves. These notes provide an introduction to some aspects of the …
form clusters as time evolves. These notes provide an introduction to some aspects of the …
The genealogy of branching Brownian motion with absorption
We consider a system of particles which perform branching Brownian motion with negative
drift and are killed upon reaching zero, in the near-critical regime where the total population …
drift and are killed upon reaching zero, in the near-critical regime where the total population …
Phase-type distributions in population genetics
Probability modelling for DNA sequence evolution is well established and provides a rich
framework for understanding genetic variation between samples of individuals from one or …
framework for understanding genetic variation between samples of individuals from one or …
A probabilistic proof of a weak limit law for the number of cuts needed to isolate the root of a random recursive tree
A PROBABILISTIC PROOF OF A WEAK LIMIT LAW FOR THE NUMBER OF CUTS NEEDED
TO ISOLATE THE ROOT OF A RANDOM RECURSIVE TREE 1 Introdu Page 1 Elect. Comm. in …
TO ISOLATE THE ROOT OF A RANDOM RECURSIVE TREE 1 Introdu Page 1 Elect. Comm. in …
A limiting distribution for the number of cuts needed to isolate the root of a random recursive tree
Let Xn be the number of cuts needed to isolate the root in a random recursive tree with n
vertices. We provide a weak convergence result for Xn. The basic observation for its proof is …
vertices. We provide a weak convergence result for Xn. The basic observation for its proof is …
[HTML][HTML] Asymptotic results for coalescent processes without proper frequencies and applications to the two-parameter Poisson–Dirichlet coalescent
M Möhle - Stochastic processes and their applications, 2010 - Elsevier
The class of coalescent processes with simultaneous multiple collisions (Ξ-coalescents)
without proper frequencies is considered. We study the asymptotic behavior of the external …
without proper frequencies is considered. We study the asymptotic behavior of the external …
Asymptotic results on the length of coalescent trees
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 …
related coalescents. This allows us to give the asymptotic distribution of the number of …
On the Number of Collisions in -Coalescents
A Gnedin, Y Yakubovich - Electronic Journal of Probability, 2007 - projecteuclid.org
We examine the total number of collisions $ C_n $ in the $\Lambda $-coalescent process
which starts with $ n $ particles. A linear growth and a stable limit law for $ C_n $ are shown …
which starts with $ n $ particles. A linear growth and a stable limit law for $ C_n $ are shown …
The asymptotic distribution of the length of beta-coalescent trees
G Kersting - 2012 - projecteuclid.org
We derive the asymptotic distribution of the total length L_n of a Beta(2-α,α)-coalescent tree
for 1<α<2, starting from n individuals. There are two regimes: If α≤12(1+5), then L_n …
for 1<α<2, starting from n individuals. There are two regimes: If α≤12(1+5), then L_n …
Asymptotics of the allele frequency spectrum associated with the Bolthausen-Sznitman coalescent
AL Basdevant, C Goldschmidt - 2008 - projecteuclid.org
We consider a coalescent process as a model for the genealogy of a sample from a
population. The population is subject to neutral mutation at constant rate ρ per individual …
population. The population is subject to neutral mutation at constant rate ρ per individual …