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

Schmidt, Klaus

doi:10.1090/S0002-9947-97-01938-7

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

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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