Poisson approximation for large clusters in the supercritical FK model

Olivier Couronné (1)

1 MODAL'X - Modélisation aléatoire de Paris X

Using the Chen-Stein method, we show that the spatial distribution of large finite clusters in the supercritical FK model approximates a Poisson process when the ratio weak mixing property holds.

Mots clés: FK percolation; Chen-Stein method; ratio weak mixing

Domaines: Probabilités [math.PR]

Olivier Couronné. Poisson approximation for large clusters in the supercritical FK model. Markov Processes And Related Fields, 2006, 12 (4), pp.627-643. ⟨hal-00149390⟩