Minimal Clade Size in the Bolthausen-Sznitman Coalescent

@article{Freund2014MinimalCS,
  title={Minimal Clade Size in the Bolthausen-Sznitman Coalescent},
  author={Fabian Freund and Arno Siri-J{\'e}gousse},
  journal={Journal of Applied Probability},
  year={2014},
  volume={51},
  pages={657 - 668}
}
In this article we show the asymptotics of distribution and moments of the size X n of the minimal clade of a randomly chosen individual in a Bolthausen-Sznitman n-coalescent for n → ∞. The Bolthausen-Sznitman n-coalescent is a Markov process taking states in the set of partitions of {1, …, n}, where 1, …, n are referred to as individuals. The minimal clade of an individual is the equivalence class the individual is in at the time of the first coalescence event this individual participates in… 
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10 Citations
Background Citations
3
Methods Citations
1

10 Citations

Asymptotics of the Minimal Clade Size and Related Functionals of Certain Beta-Coalescents
The Beta(2−α,α) n-coalescent with 1<α<2 is a Markov process taking values in the set of partitions of {1,…,n}. It evolves from the initial value {1},…,{n} by merging (coalescing) blocks together into…
-coalescents and stable Galton-Watson trees
. Representation of coalescent process using pruning of trees has been used by Goldschmidt and Martin for the Bolthausen-Sznitman coalescent and by Abraham and Delmas for the β (3 / 2 , 1 /…
$\beta$-coalescents and stable Galton-Watson trees
Representation of coalescent process using pruning of trees has been used by Goldschmidt and Martin for the Bolthausen-Sznitman coalescent and by Abraham and Delmas for the…
The minimal observable clade size of exchangeable coalescents
TLDR
This variable gives an upper bound for the minimal clade size [2], which is not observable in real data but has been shown to be useful to lower classification errors in genealogical model selection.
A Note on the Small-Time Behaviour of the Largest Block Size of Beta n -Coalescents
We study the largest block size of Beta n-coalescents at small times as n tends to infinity, using the paintbox construction of Beta-coalescents and the link between continuous-state branching…
Selection and Coalescence in a Finite State Model
To introduce selection into a model of coalescence, I explore the use of modified integer partitions that allow the identification of a preferred lineage. I show that a partition-partition transition…
On the size of the block of 1 for $\varXi$-coalescents with dust
We study the frequency process $f_1$ of the block of 1 for a $\varXi$-coalescent $\varPi$ with dust. If $\varPi$ stays infinite, $f_1$ is a jump-hold process which can be expressed as a sum of broken…
Distinguishing coalescent models - which statistics matter most?
TLDR
A random forest based Approximate Bayesian Computation is used to disentangle the effects of different statistics on distinguishing between various classes of genealogy models and a new statistic, the minimal observable clade size, is introduced to inferring whether genealogies feature multiple mergers.
Journal of Applied Probability Volume 51 (2014): Index
  • Mathematics
    Journal of Applied Probability
  • 2014
pages Albrecher, H., Boxma, O. J. and Ivanovs, J. On simple ruin expressions in dependent Sparre Andersen risk models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .…
Comportement en temps petits des Λ n-coalescents avec l'accent sur les longueurs des branches externes
Le Λ-coalescent est un processus stochastique utilise pour modeliser l'arbre genealogique d'une population composee d'une infinite d'individus, admettant des collisions multiples de lignages. Motivee…

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THE COALESCENT
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