Séminaire du 20 janvier 2003, Philippe Flajolet, Projet Algorithmes, Inria, Rocquencourt

Analytic Urns

This talk describes a purely analytic approach to urn models of the generalized P\'olya-Eggenberger type, with \emph{two} types of balls and constant balance'' (i.e., constant row sum). The treatment combines a basic partial differential equation associated with a combinatorial renormalization of the model and bases itself on elementary conformal mapping arguments.

Analytic consequences are new representations for the probability distribution of the urn's composition at time~$n$ and an explicit determination of the associated large deviation function. In particular, several urn models in the class are shown to admit of explicit representations in terms of Weierstra{\ss} elliptic functions. (Joint work with J. Gabarro and H. Pekari.)

Virginie Collette