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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Invariant cocycles, random tilings and the super-$K$ and strong Markov properties


Author: Klaus Schmidt
Journal: Trans. Amer. Math. Soc. 349 (1997), 2813-2825
MSC (1991): Primary 28D99, 60G09, 60J10, 60J15
MathSciNet review: 1422910
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Abstract: We consider $1$-cocycles with values in locally compact, second countable abelian groups on discrete, nonsingular, ergodic equivalence relations. If such a cocycle is invariant under certain automorphisms of these relations, we show that the skew product extension defined by the cocycle is ergodic. As an application we obtain an extension of many recent results of the author and K. Petersen to higher-dimensional shifts of finite type, and prove a transitivity result concerning rearrangements of certain random tilings.


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Additional Information

Klaus Schmidt
Affiliation: Mathematics Institute, University of Vienna, Strudlhofgasse 4, A-1090 Vienna, Austria; Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, A-1090 Vienna, Austria
Email: klaus.schmidt@univie.ac.at

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01938-7
PII: S 0002-9947(97)01938-7
Received by editor(s): January 30, 1996
Article copyright: © Copyright 1997 American Mathematical Society