A necessary and sufficient condition for the -coalescent to come down from the infinity.
Coalescents with simultaneous multiple collisions.
Waiting for mutations.
Alpha-stable branching and beta-coalescents.
Small-time behavior of beta coalescents
For a finite measure on [0, 1], the -coalescent is a coalescent process such that, whenever there are clusters, each -tuple of clusters merges into one at rate (1−) (d). It has recently been shown that if 1<<2, the -coalescent in which is the Beta (2−, ) distribution can be used to describe the genealogy of a continuous-state branching process (CSBP) with an -stable branching mechanism. Here we use facts...
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