STOR Colloquium: Noah Forman, University of Oxford

Exchangeability and continuum random trees

A sequence of random variables is exchangeable if its distribution is invariant under finite permutations of indices. De Finetti showed that such sequences may be viewed as a mixtures of i.i.d. (independent, identically distributed) sequences. The Chinese restaurant process (CRP) is a simple model related to many exchangeable objects, which has recently gained prominence in connection with the clustering problem in machine learning. Continuum random trees (CRTs), on the other hand, are related to various models (branching, fragmentation, coalescence) that have arisen from population genetics. This talk discusses connections between CRPs and CRTs. We focus on ongoing research concerning a Chinese restaurant with reseating that arises within a randomly evolving tree, and the continuum limits of these processes, with far-flung connections to Lévy process local times, excursion theory, and Wright-Fisher diffusions.