Persi Diaconis (Stanford University)

will speak on

Probability in the trees

Time: 3:30PM
Date: Wed 26th February 2025
Location: E0.32 (beside Pi restaurant) [map]

Abstract: What does a typical tree on n vertices 'look like'? Everybody knows that there are n^(n-2) such (I'll take trees to be rooted and call them Cayley trees). What's the diameter, max degree, width, height??? There is a second class of trees; Polya trees--unlabeled trees on n vertices. There are no formulas for these but the same questions remain. As I'll explain, Aldous' continuum random tree offers limiting answers to some of these questions. Do these limits have anything to do with 'reality'? (say n= 1,000 or n=1,000,000).
In joint work with Laurent Bartholdi, we have a new way to generate Polya trees at random. The math behind this is interesting (Burnside process, automorphism groups of trees) and we can 'actually do it' to compare Cayley, Polya, Aldous and 'reality'. The answers are unsettling and, as usual, suggest more questions. I'll try to explain all this in 'mathematical English' to a non-specialist audience.

(This talk is part of the Probability series.)

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