Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
Wolfgang Löhr (Universität Duisburg-Essen)
Markov chains on sets of (finite, graph-theoretic) trees arise in applications, e.g., as evolving genealogical trees in population models or in Markov chain Monte Carlo methods for the reconstruction of phylogenetic trees.
In order to find useful limit processes as the trees become large, we need an appropriate state space including ``continuum trees''. I will compare the more classical approach with metric measure trees and a new approach with algebraic measure trees. A particular example will be the Aldous chain on cladograms which converges in the new state space to an ergodic diffusion.
(Joint work with Leonid Mytnik and Anita Winter)