Wright-Fisher model with negative mutation rates

ABSTRACT:
An n-leaf cladogram is an unrooted tree with n leaves and every internal 
vertex of degree three. David Aldous introduced a natural Markov chain on 
the space of Cladograms that consists of picking a leaf at random and 
randomly re-attaching it to one of the remaining edges. As n grows to 
infinity this diffusion, suitably rescaled in time, is conjectured to 
converge to a diffusion on the space of continuum trees. We talk about the 
local structure of the limiting diffusion seen from the point of view of 
finitely many branch points. Locally it is a finite dimensional diffusion 
with state space in the unit simplex and is not reversible. However we 
show how it is related to another famous Markov chain model, the 
Wright-Fisher model, which consists of sampling balls of different colors 
from one urn to fill another. The key seems to be interpreting these 
diffusions as functions of Galton-Watson trees with immigration. As a 
benefit of working with diffusions explicit calculations are easy to 
derive.

BIO:
Soumik Pal did his undergraduate at the Indian Statistical Institute in 
Kolkata, and got his Ph.D. at the statistics department of Columbia 
University, under the supervision of I. Karatzas in 2006.  After a postdoc 
at Cornell, he became a professor in the math department at UW in 2008.