Year: 2008
Type: article
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.
Authors: ÉLISE JANVRESSE, THIERRY DE LA RUE
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2050872291