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Aldous diffusion on continuum trees

Banff International Research Station for Mathematical Innovation and Discovery

Consider a binary tree with n labeled leaves. Randomly select a leaf for removal and then reinsert it back on an edge selected at random from the remaining structure. This produces a Markov chain on the space of n-leaved binary trees whose invariant distribution is the uniform distribution. David Aldous, who introduced and analyzed this Markov chain, conjectured the existence of a continuum limit of this process if we remove labels from leaves, scale edge- length and time appropriately with n, and let n go to infinity. The conjectured diffusion will have an invariant distribution given by the so-called Brownian Continuum Random Tree. In a series of papers, co-authored with N. Forman, D. Rizzolo, and M. Winkel, we construct this continuum limit. This talk will be an overview of our construction and describe the path behavior of this limiting object.

Mathematics; Probability theory and stochastic processes; Potential theory; Probability / statistical mechanics

video/mp4

Author affiliation: University of Washington

2018-04-24

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/65602

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/