For n ≥ 1 we consider the class JP(n) of dynamical systems each of whose ergodic joinings with a Cartesian product of k weakly mixing automorphisms (k ≥ n) can be represented as the independent extension of a joining of the system with only n coordinate factors. For n ≥ 2 we show that, whenever the maximal spectral type of a weakly mixing automorphism T is singular with respect to the convolution of any n continuous measures, i.e. T has the so-called convolution singularity property of order n, then T belongs to JP(n-1). To provide examples of such automorphisms, we exploit spectral simplicity on symmetric Fock spaces. This also allows us to show that for any n ≥ 2 the class JP(n) is essentially larger than JP(n-1). Moreover, we show that all members of JP(n) are disjoint from ergodic automorphisms generated by infinitely divisible stationary processes.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-2-2,
author = {Joanna Ku\l aga-Przymus and Fran\c cois Parreau},
title = {Disjointness properties for Cartesian products of weakly mixing systems},
journal = {Colloquium Mathematicae},
volume = {126},
year = {2012},
pages = {153-177},
zbl = {1268.37005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-2-2}
}
Joanna Kułaga-Przymus; François Parreau. Disjointness properties for Cartesian products of weakly mixing systems. Colloquium Mathematicae, Tome 126 (2012) pp. 153-177. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-2-2/