School of Mathematical Sciences

The collision spectrum of Lambda-coalescents menu

The collision spectrum of Lambda-coalescents

Alexander Gnedin (QMUL)
Wed, 01/11/2017 - 13:00
W316, Queen's Building

Lambda-coalescents model the evolution of a coalescing system in which any number of blocks
randomly sampled from the whole may merge into a larger block. There is a variety of quantitatively
different behaviours of this process depending on the concentration of the directing measure near zero.
In particular, different limiting distributions appear for the total number of collisions in the coalescent starting with $n$ singleton blocks. In this talk we survey available results on the number of collisions and
then focus on recent findings on more delicate collision spectrum $(X_{n,k} : 2 \leq k\leq\leq n)$, where $X_{n,k}$ is the number of $k$-fold collisions. This is a joint work with A. Iksanov, A. Marynych and M. Moehle.