Horton self-similarity of Kingman's coalescent tree

Yevgeniy Kovchegov; Ilya Zaliapin

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arXiv · 1207.7108

Horton self-similarity of Kingman's coalescent tree

Yevgeniy Kovchegov·Ilya Zaliapin

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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.

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BibTeX RIS

Yevgeniy Kovchegov, Ilya Zaliapin. 2012-07-30. Horton self-similarity of Kingman's coalescent tree. https://arxiv.org/abs/1207.7108

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