Random recursive trees and the bolthausen-sznitman coalescent

56Citations
Citations of this article
13Readers
Mendeley users who have this article in their library.

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 → ∞, 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 → ∞. 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. © 2005 Applied Probability Trust.

Cite

CITATION STYLE

APA

Goldschmidt, C., & Martin, J. B. (2005). Random recursive trees and the bolthausen-sznitman coalescent. Electronic Journal of Probability, 10, 718–745. https://doi.org/10.1214/EJP.v10-265

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free