Seminar by Noah Forman

Please Note: This seminar will be held in-person.

The diffusion analogue to a tree-valued Markov chain

In '99, David Aldous conjectured that a certain natural Markov chain on the space of binary combinatorial trees should have a continuum analogue, which would be a continuum-tree-valued diffusion - a continuous stochastic process on a space of tree-like metric spaces. This talk discusses work by F-Pal-Rizzolo-Winkel that has verified this conjecture with a path-wise construction of the diffusion. Our approach explores connections between tree growth processes, the Chinese restaurant process, Galton-Watson and Crump-Mode-Jaegers branching processes, Wright-Fisher diffusions, and stable Lévy processes.