Universiteit Utrecht

Department of Mathematics

Collisions in Λ-coalescent

Yuri Yakubovich

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.

Back to the history of the seminar or the Colloquium Stochastiek homepage.
Yuri Yakubovich