Tel Aviv University
Dear all,
This week at the Horowitz seminar on Probability, Ergodic Theory and
Dynamical Systems at Tel Aviv University we are happy to have:
Speaker: Anita Winter, Universit\"at Duisburg-Essen
Title: The Aldous move on cladograms in the diffusion limit
Date: Monday, January 2
Time: 14:30
Place: Schreiber 309
(back to the usual time and place)
A n-phylogenetic tree is a semi-labeled, unrooted and binary tree
with n leaves labeled 1,2,...,n and with (n-2) unlabeled internal
leaves and positive edge lengths representing the time spans between
common ancestors. In biological systematics phylogenetic trees are
used to represent the evolutionary relationship between species. If
one does focus only on the kinship (that is taking all edge length of
unit length), a more precise term is cladogram.
Aldous constructed a Markov chain on cladograms and gave bounds on
their mixing time. On the other hand, Aldous also gave a notion of
convergence of cladograms which shows that the uniform cladogram with
N leaves and edge length re-scaled by a factor of 1/sqrt{N} converges
to the so-called Continuum Random Tree (CRT). These two results
suggest that if we re-scale edge lengths by a factor of 1/\sqrt{N}
and speeding up time by a factor of N^{3/2} the Aldous move on
cladograms converges in some sense to a continuous tree-valued
diffusion. We will use Dirichlet form methods to construct limiting
dynamics. (This is joint work with Leonid Mytnik, Technion Haifa)
Best regards,


Seminar webpage:

Technion Math Net-2 (TECHMATH2)
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