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Incorporating a collection of recent results, Polya Urn Models deals with discrete probability through the modern and evolving urn theory and its numerous applications.

The book first substantiates the realization of distributions with urn arguments and introduces several modern tools, including exchangeability and stochastic processes via urns. It reviews classical probability problems and presents dichromatic Polya urns as a basic discrete structure growing in discrete time. The author then embeds the discrete Polya urn scheme in Poisson processes to achieve an equivalent view in...

Incorporating a collection of recent results, Pólya Urn Models deals with discrete probability through the modern and evolving urn theory and its numerous applications. It looks at how some classical problems of discrete probability have roots in urn models.

The subject is at the crossroads of Discrete Mathematics and Computer Science, with a strong probabilistic flavor. The main tools used before are on the one hand analytic (generating functions and complex analysis), and on the other probabilistic (strong laws, central limit theorems, martingales, etc.) Often, professionals worked with one set of tools or the other. We offer a reconciliation to espouse these fields to come in hand-in-hand offering a harmonious and beneficial marriage.