# $\beta$-coalescents and stable Galton-Watson trees

@article{Abraham2013betacoalescentsAS, title={\$\beta\$-coalescents and stable Galton-Watson trees}, author={Romain Abraham and Jean-François Delmas}, journal={ALEA-Latin American Journal of Probability and Mathematical Statistics}, year={2013}, volume={12}, pages={451-476} }

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 $\beta(3/2,1/2)$-coalescent. By considering a pruning procedure on stable Galton-Watson tree with $n$ labeled leaves, we give a representation of the discrete $\beta(1+\alpha,1-\alpha)$-coalescent, with $\alpha\in [1/2,1)$ starting from the trivial partition of the $n$ first integers. The construction can also be made…

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