| | |
| | |
Stat |
Members: 3643 Articles: 2'487'895 Articles rated: 2609
29 March 2024 |
|
| | | |
|
Article overview
| |
|
Random recursive trees and the Bolthausen-Sznitman coalescent | Christina Goldschmidt
; James B. Martin
; | Date: |
13 Feb 2005 | Journal: | Electron. J. Probab. Vol. 10 (2005) paper 21, pp. 718-745 | Subject: | Probability; Combinatorics MSC-class: 60J25 (Primary) 60C05, 60F05, 05C05 (Secondary) | math.PR math.CO | 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 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. | Source: | arXiv, math.PR/0502263 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser claudebot
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |