@article{ECP2872,
author = {Harry Crane},
title = {Consistent Markov branching trees with discrete edge lengths},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {18},
year = {2013},
keywords = {Markov branching model; homogeneous fragmentation process; splitting rule; dislocation measure; sampling consistency; exchangeable random partition; weighted tree; random tree},
abstract = {We study consistent collections of random fragmentation trees with random integer-valued edge lengths. We prove several equivalent necessary and sufficient conditions under which Geometrically distributed edge lengths can be consistently assigned to a Markov branching tree. Among these conditions is a characterization by a unique probability measure, which plays a role similar to the dislocation measure for homogeneous fragmentation processes. We discuss this and other connections to previous work on Markov branching trees and homogeneous fragmentation processes.},
pages = {no. 73, 1-14},
issn = {1083-589X},
doi = {10.1214/ECP.v18-2872},
url = {http://ecp.ejpecp.org/article/view/2872}}