The compound Poisson distribution and return times in dynamical systems

Nicolai Haydn (1) , Sandro Vaienti (2, 3)

1 USC - University of Southern California
2 CPT - Centre de Physique Théorique - UMR 6207
3 CPT - Centre de Physique Théorique - UMR 7332

Previously it has been shown that some classes of mixing dynamical systems have limiting return times distributions that are almost everywhere Poissonian. Here we study the behaviour of return times at periodic points and show that the limiting distribution is a compound Poissonian distribution. We also derive error terms for the convergence to the limiting distribution. We also prove a very general theorem that can be used to establish compound Poisson distributions in many other settings.

Mots clés: Poisson distribution; recurrence; mixing

Domaines: Systèmes dynamiques [math.DS]

Nicolai Haydn, Sandro Vaienti. The compound Poisson distribution and return times in dynamical systems. Probability Theory and Related Fields, 2009, 144 (3-4), pp.517-542. ⟨hal-00285201⟩