Isomorphism and symmetries in random phylogenetic trees
Miklós Bóona and PHILIPPE FLAJOLET
Source: J. Appl. Probab. Volume 46, Number 4
(2009), 1005-1019.
Abstract
The probability that two randomly selected phylogenetic trees of the same size are isomorphic is found to be asymptotic to a decreasing exponential modulated by a polynomial factor. The number of symmetrical nodes in a random phylogenetic tree of large size obeys a limiting Gaussian distribution, in the sense of both central and local limits. The probability that two random phylogenetic trees have the same number of symmetries asymptotically obeys an inverse square-root law. Precise estimates for these problems are obtained by methods of analytic combinatorics, involving bivariate generating functions, singularity analysis, and quasi-powers approximations.
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Keywords: Analytic combinatorics; combinatorial probability; generating function; isomorphism problem; limit distributions; nonplane tree; phylogenies; random tree; singularity analysis; symmetries and automorphisms
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Permanent link to this document: http://projecteuclid.org/euclid.jap/1261670685
Digital Object Identifier: doi:10.1239/jap/1261670685
Mathematical Reviews number (MathSciNet): MR2582703
Zentralblatt MATH identifier: 05665452
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