Beta-coalescents and continuous stable random trees
نویسندگان
چکیده
منابع مشابه
Beta-coalescents and continuous stable random trees
Coalescents with multiple collisions, also known as Λ-coalescents, were introduced by Pitman and Sagitov in 1999. These processes describe the evolution of particles that undergo stochastic coagulation in such a way that several blocks can merge at the same time to form a single block. In the case that the measure Λ is the Beta(2 − α, α) distribution, they are also known to describe the genealo...
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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, 1/2)-coalescent. By considering a pruning procedure on stable GaltonWatson tree with n labeled leaves, we give a representation of the discrete β(1 + α, 1− α)coalescent, with α ∈ [1/2, 1) starting from the trivial par...
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We determine that the continuous-state branching processes for which the genealogy, suitably time-changed, can be described by an autonomous Markov process are precisely those arising from α-stable branching mechanisms. The random ancestral partition is then a time-changed Λ-coalescent, where Λ is the Beta-distribution with parameters 2− α and α, and the time change is given by Z1−α, where Z is...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2007
ISSN: 0091-1798
DOI: 10.1214/009117906000001114