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 squareroot law. Precise estimates for these problems are obtained by methods of analytic combinatorics, involving bivariate generating functions, singularity analysis, and quasipowers approximations.
 Publication:

arXiv eprints
 Pub Date:
 January 2009
 arXiv:
 arXiv:0901.0696
 Bibcode:
 2009arXiv0901.0696B
 Keywords:

 Mathematics  Probability;
 Mathematics  Combinatorics;
 60C05;
 05A16
 EPrint:
 14 pages