On Polya-Friedman random walks

Thierry Huillet (1)

1 LPTM - UMR 8089 - Laboratoire de Physique Théorique et Modélisation

The P\'{o}lya process is an urn scheme arising in the context of the contagion spreading. It exhibits unstable persistence effects. The Friedman urn process is dual to the P\'{o}lya one with antipersistent stabilizing effects. It appears in a safety campaign problem. A P\'{o}lya-Friedman urn process is investigated with a tuning persistence parameter extrapolating the latter two extreme processes. The study includes the diffusion approximations of both the P\'{o}lya-Friedman proportion process and the population gap random walk. The structure of the former is a generalized Wright-Fisher diffusion appearing in Population Genetics. The correlation structure of the latter presents an anomalous character at a critical value of the persistence parameter.

Mots clés: Polya-Friedman urns; random walks; persistence; Wright-Fisher model; New applications of statistical mechanics; Non-equilibrium processes.; Non-equilibrium processes

Domaines: Mécanique statistique [cond-mat.stat-mech]

Thierry Huillet. On Polya-Friedman random walks. Journal of Physics A: Mathematical and Theoretical, 2008, 41 (50), pp.505005 doi: 10.1088/1751-8113/41/50/505005. ⟨hal-00331517⟩