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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Invariant cocycles, random tilings and the super-$K$ and strong Markov properties
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by Klaus Schmidt PDF
Trans. Amer. Math. Soc. 349 (1997), 2813-2825 Request permission


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:
  • Received by editor(s): January 30, 1996
  • © Copyright 1997 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 349 (1997), 2813-2825
  • MSC (1991): Primary 28D99, 60G09, 60J10, 60J15
  • DOI:
  • MathSciNet review: 1422910