English

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 1/2\leq 1/2; otherwise, it is called large).

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Cite

@article{arxiv.math/0605472,
  title  = {An algebraic approach to Polya processes},
  author = {Nicolas Pouyanne},
  journal= {arXiv preprint arXiv:math/0605472},
  year   = {2015}
}