An algebraic approach to Polya processes

Abstract

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

References in corpus (3)

• Analytic urns
• Congruence properties of depths in some random trees
• The space requirement of m-ary search trees: distributional asymptotics for m >= 27

Cited by in corpus (3)

• Limit distributions for large Pólya urns
• Polya urns via the contraction method
• Mean and variance of balanced Pólya urns