The collision spectrum of $\Lambda$-coalescents

@article{Gnedin2018TheCS,
  title={The collision spectrum of \$\Lambda\$-coalescents},
  author={Alexander V. Gnedin and Alexander Iksanov and Alexander Marynych and Martin Mohle},
  journal={The Annals of Applied Probability},
  year={2018}
}
$\Lambda$-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. For the coalescent restricted to initially $n$ singletons we study the collision spectrum $(X_{n,k}:2\le k\le n)$, where $X_{n,k}$ counts, throughout the history of the process, the number of collisions involving exactly $k$ blocks. Our focus is on the large $n$ asymptotics of the joint distribution of the $X_{n,k}$'s, as well as on… 

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