%0 Journal Article
%T An algebraic approach to Polya processes
%A Nicolas Pouyanne
%J Mathematics
%D 2006
%I arXiv
%R 10.1214/07-AIHP130
%X P\'olya processes are natural generalization of P\'olya-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 P\'olya process is called {\it small} when 1 is simple eigenvalue of its replacement matrix and when any other eigenvalue has a real part $\leq 1/2$; otherwise, it is called large).
%U http://arxiv.org/abs/math/0605472v2