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

Author:
Klaus Schmidt

Journal:
Trans. Amer. Math. Soc. **349** (1997), 2813-2825

MSC (1991):
Primary 28D99, 60G09, 60J10, 60J15

DOI:
https://doi.org/10.1090/S0002-9947-97-01938-7

MathSciNet review:
1422910

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider -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:
https://doi.org/10.1090/S0002-9947-97-01938-7

Received by editor(s):
January 30, 1996

Article copyright:
© Copyright 1997
American Mathematical Society