The structure of the allelic partition of the total population for Galton-Watson processes with neutral mutations

Abstract : We consider a (sub) critical Galton-Watson process with neutral mutations (infinite alleles model), and decompose the entire population into clusters of individuals carrying the same allele. We specify the law of this allelic partition in terms of the distribution of the number of clone-children and the number of mutant-children of a typical individual. The approach combines an extension of Harris representation of Galton-Watson processes and a version of the ballot theorem. Some limit theorems related to the distribution of the allelic partition are also given.
Type de document :
Pré-publication, Document de travail
This version corrects a significant mistake in the first one. 2009
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https://hal.archives-ouvertes.fr/hal-00191132
Contributeur : Jean Bertoin <>
Soumis le : vendredi 28 août 2009 - 18:44:59
Dernière modification le : lundi 29 mai 2017 - 14:24:43
Document(s) archivé(s) le : jeudi 23 septembre 2010 - 18:02:40

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aop441.pdf
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  • HAL Id : hal-00191132, version 3
  • ARXIV : 0711.3852

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INSMI | UPMC | PSL | USPC | PMA

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Jean Bertoin. The structure of the allelic partition of the total population for Galton-Watson processes with neutral mutations. This version corrects a significant mistake in the first one. 2009. <hal-00191132v3>

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