Horton self-similarity of Kingman's coalescent tree
Probability
2015-09-29 v5 Mathematical Physics
Classical Analysis and ODEs
Combinatorics
math.MP
Abstract
The paper establishes a weak version of Horton self-similarity for a tree representation of Kingman's coalescent process. The proof is based on a Smoluchowski-type system of ordinary differential equations for the number of branches of a given Horton-Strahler order in a tree that represents Kingman's N-coalescent process with a constant kernel, in a hydrodynamic limit. We also demonstrate a close connection between the combinatorial Kingman's tree and the combinatorial level set tree of a white noise, which implies Horton self-similarity for the latter.
Keywords
Cite
@article{arxiv.1207.7108,
title = {Horton self-similarity of Kingman's coalescent tree},
author = {Yevgeniy Kovchegov and Ilya Zaliapin},
journal= {arXiv preprint arXiv:1207.7108},
year = {2015}
}