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A class of pairwise-independent joinings

Published online by Cambridge University Press:  01 October 2008

ÉLISE JANVRESSE  and
THIERRY DE LA RUE
ÉLISE JANVRESSE
Affiliation:
Laboratoire de Mathématiques Raphaël Salem, UMR 6085 CNRS – Université de Rouen, Avenue de l’Université, B.P. 12, F76801 Saint-Étienne-du-Rouvray Cedex, France (email: [email protected], [email protected])
THIERRY DE LA RUE
Affiliation:
Laboratoire de Mathématiques Raphaël Salem, UMR 6085 CNRS – Université de Rouen, Avenue de l’Université, B.P. 12, F76801 Saint-Étienne-du-Rouvray Cedex, France (email: [email protected], [email protected])
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Abstract

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 two-fold mixing implies three-fold-mixing.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 5 , October 2008 , pp. 1545 - 1557
Copyright
Copyright © 2008 Cambridge University Press

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