Chaoticity for multi-class systems and exchangeability within classes

Carl Graham (1)

1 CMAP - Centre de Mathématiques Appliquées

Under the natural partial exchangeability assumption for multi-class interacting particle systems, we prove that these converge to an independent system with infinite i.i.d. classes if and only if the empirical measure of each class satisfies a weak law of large numbers. This extension of a classical result for exchangeable systems (related to the de Finetti Theorem) is somewhat surprising, since then convergence of each class to infinite i.i.d. particles implies asymptotic independence of particles of different classes.

Mots clés: Multiclass; multitype; multispecies; or multipopulation interacting particle systems; partial exchangeability; chaoticity; weak law of large numbers for empirical measures; de Finetti Theorem

Domaines: Probabilités [math.PR]

Carl Graham. Chaoticity for multi-class systems and exchangeability within classes. 2007. ⟨hal-00171668v1⟩