Random walks on a space of trees with integer edge weights
Consider the Markov process in the space of binary trees in
which, at each step, you delete a random leaf and then grow a new leaf in a
random location on the tree. In 2000, Aldous conjectured that it should
have a continuum analogue, which would be a continuum random tree-valued
diffusion. We will discuss a family of projectively consistent Markov
chains that are projections of this tree, and discuss how these
representations can be passed to the continuum. This is joint work with
Soumik Pal, Douglas Rizzolo, and Matthias Winkel.