%0 Journal Article %1 MR2546753 %A Bertoin, Jean %D 2009 %J Ann. Probab. %K branching_processes ewens_sampling_formula neutral_variation partitions %N 4 %P 1502--1523 %R 10.1214/08-AOP441 %T The structure of the allelic partition of the total population for Galton-Watson processes with neutral mutations %U http://dx.doi.org/10.1214/08-AOP441 %V 37 %X We consider a (sub-)critical Galton­Watson process with neutral muta- tions (infinite alleles model), and decompose the entire population into clus- ters 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 Galton­Watson processes and a version of the ballot theorem. Some limit theorems related to the distribution of the allelic partition are also given.

@article{MR2546753, abstract = { We consider a (sub-)critical Galton­Watson process with neutral muta- tions (infinite alleles model), and decompose the entire population into clus- ters 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 Galton­Watson processes and a version of the ballot theorem. Some limit theorems related to the distribution of the allelic partition are also given. }, added-at = {2009-11-19T18:49:39.000+0100}, author = {Bertoin, Jean}, biburl = {https://www.bibsonomy.org/bibtex/25c1a3a7879fe385019cc39dfb0466882/peter.ralph}, coden = {APBYAE}, description = {MR: Publications results for "MR Number=(2546753)"}, doi = {10.1214/08-AOP441}, fjournal = {The Annals of Probability}, interhash = {177b89240823bedfa449c7e977ecbec1}, intrahash = {5c1a3a7879fe385019cc39dfb0466882}, issn = {0091-1798}, journal = {Ann. Probab.}, keywords = {branching_processes ewens_sampling_formula neutral_variation partitions}, mrclass = {60J80}, mrnumber = {MR2546753}, number = 4, pages = {1502--1523}, timestamp = {2009-11-19T18:49:39.000+0100}, title = {The structure of the allelic partition of the total population for {G}alton-{W}atson processes with neutral mutations}, url = {http://dx.doi.org/10.1214/08-AOP441}, volume = 37, year = 2009 }