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) Abstract: 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, Ron Seminar webpage: <http://www.math.tau.ac.il/~peledron/Horowitz_seminar/Horowitz_seminar.html> --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Ron Peled <peledron@gmail.com>