An algebraic approach to Polya processes
<|reference_start|>An algebraic approach to Polya processes: 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).<|reference_end|>
@article{pouyanne2006an,
    title={An algebraic approach to Polya processes},
    author={Nicolas Pouyanne (LM-Versailles)},
    journal={Annales de l'IHP - Probabilit\'es et Statistiques (2008) Vol. 44,
  No. 2, 293-323},
    year={2006},
    doi={10.1214/07-AIHP130},
    archivePrefix={arXiv},
    eprint={math/0605472},
    primaryClass={math.CO cs.DM cs.DS math.PR}
}