An algebraic approach to Polya processes
Nicolas Pouyanne
Abstract
Pólya processes are natural generalization of Pólya-Eggenberger urn models. This article presents a new approach of their asymptotic behaviour via moments, based on the spectral decomposition of a suitable finite difference operator on polynomial functions. Especially, it provides new results for large processes (a Pólya process is called small when 1 is simple eigenvalue of its replacement matrix and when any other eigenvalue has a real part ≤ 1/2; otherwise, it is called large).
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