Probability Seminar: A new approach to classical P\'{o}lya and its infinite color generalization

15 January 2021 13:00 in Zoom

In this work, we introduce a generalization of the classical P\'{o}lya urn scheme with colors indexed by a Polish space, say, $S$.
The urns are defined as random finite measures on $S$ endowed with the Borel $\sigma$-algebra, say, $\SS$. The generalization is
an extension of a model introduced earlier by Blackwell and MacQueen (1973). We introduce a new approach of representing the observed sequence of colors from such a scheme in terms of an associated branching Markov chain on the random recursive tree. This embedding enables us to obtain weak convergence of the random measures induced by the urns. The coupling reveals that the weak convergence is completely guided by the Markov chain associated with the replacement matrix of the urn.
This talk is based on two joint works with Antar Bandyopadhyay and Svante Janson.

Contact ellen.g.powell@durham.ac.uk for more information