@article{EJP265,
author = {Christina Goldschmidt and James Martin},
title = {Random Recursive Trees and the Bolthausen-Sznitman Coalesent},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {10},
year = {2005},
keywords = {},
abstract = {We describe a representation of the Bolthausen-Sznitman coalescent in terms of the cutting of random recursive trees. Using this representation, we prove results concerning the final collision of the coalescent restricted to $[n]$: we show that the distribution of the number of blocks involved in the final collision converges as $n\to\infty$, and obtain a scaling law for the sizes of these blocks. We also consider the discrete-time Markov chain giving the number of blocks after each collision of the coalescent restricted to $[n]$; we show that the transition probabilities of the time-reversal of this Markov chain have limits as $n\to\infty$. These results can be interpreted as describing a ``post-gelation'' phase of the Bolthausen-Sznitman coalescent, in which a giant cluster containing almost all of the mass has already formed and the remaining small blocks are being absorbed.},
pages = {no. 21, 718-745},
issn = {1083-6489},
doi = {10.1214/EJP.v10-265},
url = {http://ejp.ejpecp.org/article/view/265}}