Zero Krengel Entropy does not kill Poisson Entropy

Élise Janvresse (1) , Thierry de La Rue (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

We prove that the notions of Krengel entropy and Poisson entropy for infinite-measure-preserving transformations do not always coincide: We construct a conservative infinite-measure-preserving transformation with zero Krengel entropy (the induced transformation on a set of measure 1 is the Von Neumann-Kakutani odometer), but whose associated Poisson suspension has positive entropy.

Mots clés: infinite-measure-preserving transformation; Poisson suspension; Krengel entropy

Domaines: Probabilités [math.PR]; Systèmes dynamiques [math.DS]

Élise Janvresse, Thierry de La Rue. Zero Krengel Entropy does not kill Poisson Entropy. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2012, 48 (2), pp.368-376. ⟨10.1214/10-AIHP393⟩. ⟨hal-00424090v2⟩