A Class of pairwise-independent Joinings

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

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

We introduce a special class of pairwise-independent self-joinings for a stationary process: Those for which one coordinate is a continuous function of the two others. We investigate which properties on the process the existence of such a joining entails. In particular, we prove that if the process is aperiodic, then it has positive entropy. Our other results suggest that such pairwise independent, non-independent self-joinings exist only in very specific situations: Essentially when the process is a subshift of finite type topologically conjugate to a full-shift. This provides an argument in favor of the conjecture that 2-fold mixing implies 3-fold-mixing.

Mots clés: pairwise-independent joining; subshift of finite type; multifold mixing

Domaines: Probabilités [math.PR]

Elise Janvresse, Thierry de La Rue. A Class of pairwise-independent Joinings. Ergodic Theory and Dynamical Systems, 2008, 28 (5), pp.1545-1557. ⟨10.1017/S0143385707000958⟩. ⟨hal-00143357v3⟩