Random recursive trees and the Bolthausen-Sznitman coalescent
| dc.creator | Goldschmidt, Christina | |
| dc.creator | Martin, James B. | |
| dc.date | 2005-02-13 | |
| dc.date | 2005-06-02 | |
| dc.date.accessioned | 2026-07-07T05:16:56Z | |
| dc.date.available | 2026-07-07T05:16:56Z | |
| dc.description | 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 tends to infinity, 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 tends to infinity. 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. | |
| dc.description | 28 pages, 2 figures. Revised version with minor alterations. To appear in Electron. J. Probab | |
| dc.identifier | https://arxiv.org/abs/math/0502263 | |
| dc.identifier | http://arxiv.org/abs/math/0502263 | |
| dc.identifier | Electron. J. Probab. Vol. 10 (2005) paper 21, pp. 718-745 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74172 | |
| dc.subject | Probability | |
| dc.subject | Combinatorics | |
| dc.subject | 60J25 (Primary) 60C05, 60F05, 05C05 (Secondary) | |
| dc.title | Random recursive trees and the Bolthausen-Sznitman coalescent | |
| dc.type | text |