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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Joining primeness and disjointness from infinitely divisible systems


Authors: Mariusz Lemańczyk, François Parreau and Emmanuel Roy
Journal: Proc. Amer. Math. Soc. 139 (2011), 185-199
MSC (2010): Primary 37A05; Secondary 37A10, 37A30, 37A50
Published electronically: July 2, 2010
MathSciNet review: 2729082
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Abstract: We show that ergodic dynamical systems generated by infinitely divisible stationary processes are disjoint in the sense of Furstenberg from distally simple systems and systems whose maximal spectral type is singular with respect to the convolution of any two continuous measures.


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Additional Information

Mariusz Lemańczyk
Affiliation: Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87–100 Toruń, Poland
Email: mlem@mat.uni.torun.pl

François Parreau
Affiliation: Laboratoire d’Analyse, Géométrie et Applications, UMR 7539 Université Paris 13 et CNRS, 99 av. J.-B. Clément, 93430 Villetaneuse, France
Email: parreau@math.univ-paris13.fr

Emmanuel Roy
Affiliation: Laboratoire d’Analyse, Géométrie et Applications, UMR 7539 Université Paris 13 et CNRS, 99 av. J.-B. Clément, 93430 Villetaneuse, France
Email: roy@math.univ-paris13.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10457-4
PII: S 0002-9939(2010)10457-4
Keywords: Joinings, disjointness, infinite divisibility, distal simplicity, spectral singularity and convolutions
Received by editor(s): October 28, 2009
Received by editor(s) in revised form: February 22, 2010
Published electronically: July 2, 2010
Additional Notes: The research of the first author is partially supported by Polish MNiSzW grant N N201 384834, Marie Curie “Transfer of Knowledge” EU program, project MTKD-CT-2005-030042 (TODEQ)
The research of the first and third authors is partially supported by the MSRI (Berkeley) program “Ergodic Theory and Additive Combinatorics”
Communicated by: Bryna Kra
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.