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.