Disjointness properties for Cartesian products of weakly mixing systems

Joanna Kułaga-Przymus, and François Parreau. "Disjointness properties for Cartesian products of weakly mixing systems." Colloquium Mathematicae 128.2 (2012): 153-177. <http://eudml.org/doc/284268>.

@article{JoannaKułaga2012,
abstract = {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.},
author = {Joanna Kułaga-Przymus, François Parreau},
journal = {Colloquium Mathematicae},
keywords = {disjointness; joinings; spectral singularity and convolutions; spectral simplicity; infinite divisibility},
language = {eng},
number = {2},
pages = {153-177},
title = {Disjointness properties for Cartesian products of weakly mixing systems},
url = {http://eudml.org/doc/284268},
volume = {128},
year = {2012},
}

TY - JOUR
AU - Joanna Kułaga-Przymus
AU - François Parreau
TI - Disjointness properties for Cartesian products of weakly mixing systems
JO - Colloquium Mathematicae
PY - 2012
VL - 128
IS - 2
SP - 153
EP - 177
AB - 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.
LA - eng
KW - disjointness; joinings; spectral singularity and convolutions; spectral simplicity; infinite divisibility
UR - http://eudml.org/doc/284268
ER -