Isomorphism and Symmetries in Random Phylogenetic Trees
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.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2009
- DOI:
- 10.48550/arXiv.0901.0696
- arXiv:
- arXiv:0901.0696
- Bibcode:
- 2009arXiv0901.0696B
- Keywords:
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- Mathematics - Probability;
- Mathematics - Combinatorics;
- 60C05;
- 05A16
- E-Print:
- 14 pages