Gibbs partitions, Mittag Leffler functions and waiting time models

Abstract

It is known random partitions of the integers may be obtained by a process of discovery of excursion intervals of generalized notions of Bessel processes, with the most prominent example being Brownian motion or Brownian bridge. This leads to the two parameter Chinese restaurant process, which has a variety of applications. Generalizations of this scheme lead to the general class of Gibbs partitions. We examine Gibbs partitions from different perspective and describe classes of random partitions that can be expressed in terms of waiting time distributions.

Biography

Prof. Lancelot F. JAMES received his PhD degree at SUNY, Buffalo. He has published nearly 40 papers on the journals such as Annals of Statistics, Annals of Applied Probability, Journal of American Statistical Associations, Journal of Business and Economics Statistics, Bernoulli and so on.