Department of Mathematics

Collisions in Λ-coalescent

(UU)

22 May 2007

In this talk we deal with a family of coalescent processes
which are known as Λ-coalescents.
The parameter Λ is a finite measure on [0,1].
Under assumption of power-like behaviour of Λ at zero
with exponent α ∈ ]0,1[
we show that the growth of the number of collisions needed
for *n* blocks to merge in a single block grows
linearly with *n*. Furthermore, we establish
a weak limit theorem for a number of collisions:
in a proper scaling the limit distribution is a completely assymetric
stable distribution of index 2 − α.

This is a joint work with Sasha Gnedin.

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Yuri Yakubovich