Disjointness properties for Cartesian products of weakly mixing systems

• Autorzy: Joanna Kułaga-Przymus , François Parreau
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37A50: Relations with probability theory and stochastic processes
• 37A30: Ergodic theorems, spectral theory, Markov operators
• 37A05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2012
• Tom: 128
• Numer: 2
• Strony: 153-177

Daty

wydano

2012

Twórcy

autor

Joanna Kułaga-Przymus

• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

autor

François Parreau

• Laboratoire d'Analyse, Géométrie et Applications, UMR 7539, Université Paris 13 Sorbonne Paris Cité et CNRS, 99 av. J.-B. Clément, 94430 Villetaneuse, France

Identyfikatory

DOI

10.4064/cm128-2-2