An algebraic approach to Polya processes
Combinatorics
2015-06-26 v2 Discrete Mathematics
Data Structures and Algorithms
Probability
Abstract
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 ; otherwise, it is called large).
Keywords
Cite
@article{arxiv.math/0605472,
title = {An algebraic approach to Polya processes},
author = {Nicolas Pouyanne},
journal= {arXiv preprint arXiv:math/0605472},
year = {2015}
}