Asymptotic results for coalescent processes without proper frequencies and applications to the two-parameter Poisson-Dirichlet coalescent

@article{Mhle2010AsymptoticRF,
  title={Asymptotic results for coalescent processes without proper frequencies and applications to the two-parameter Poisson-Dirichlet coalescent},
  author={Martin M{\"o}hle},
  journal={Stochastic Processes and their Applications},
  year={2010},
  volume={120},
  pages={2159-2173}
}
  • M. Möhle
  • Published 1 November 2010
  • Mathematics
  • Stochastic Processes and their Applications
On the external branches of coalescents with multiple collisions
TLDR
A recursion for the joint moments of the external branch lengths for coalescents with multiple collisions (Lambda-coalescents) is provided and results show that the lengths of two randomly chosen external branches are positively correlated for the Bolthausen-Sznitman coalescent.
ON THE EXTERNAL BRANCHES OF COALESCENT PROCESSES WITH MULTIPLE COLLISIONS WITH AN EMPHASIS ON THE BOLTHAUSEN-SZNITMAN COA- LESCENT
A recursion for the joint moments of the external branch lengths for coalescents with multiple collisions (-coalescents) is provided. This recursion is used to derive asymptotic expansions as the
Genealogies of regular exchangeable coalescents with applications to sampling
TLDR
This article considers a model of genealogy corresponding to a regular exchangeable coalescent started from a large finite configuration, and undergoing neutral mutations, and derived analogous results for the number of active mutation-free lineages and the combined lineage lengths.
Scaling limits for a class of regular $\Xi$-coalescents
The block counting process with initial state n counts the number of blocks of an exchangeable coalescent (Ξ-coalescent) restricted to a sample of size n . This work provides scaling limits for the
The symmetric coalescent and Wright–Fisher models with bottlenecks
We define a new class of $\Xi$-coalescents characterized by a possibly infinite measure over the non negative integers. We call them symmetric coalescents since they are the unique family of
External branch lengths of Λ-coalescents without a dust component
Λ -coalescents model genealogies of samples of individuals from a large population by means of a family tree. The tree’s leaves represent the individuals, and the lengths of the adjacent edges
The total external length of the evolving Kingman coalescent
The evolving Kingman coalescent is the tree-valued process which records the time evolution undergone by the genealogies of Moran populations. We consider the associated process of total external
Asymptotic genealogies for a class of generalized Wright–Fisher models
We study a class of Cannings models with population size N having a mixed multinomial offspring distribution with random success probabilities W1, . . . ,WN induced by independent and identically
Absorption Time and Tree Length of the Kingman Coalescent and the Gumbel Distribution
Formulas are provided for the cumulants and the moments of the time T back to the most recent common ancestor of the Kingman coalescent. It is shown that both the jth cumulant and the jth moment of T
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    Advances in Applied Probability
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