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May 2013 Invariant monotone coupling need not exist
Péter Mester
Ann. Probab. 41(3A): 1180-1190 (May 2013). DOI: 10.1214/12-AOP767

Abstract

We show by example that there is a Cayley graph, having two invariant random subgraphs $X$ and $Y$, such that there exists a monotone coupling between them in the sense that $X\subset Y$, although no such coupling can be invariant. Here, “invariant” means that the distribution is invariant under group multiplications.

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Péter Mester. "Invariant monotone coupling need not exist." Ann. Probab. 41 (3A) 1180 - 1190, May 2013. https://doi.org/10.1214/12-AOP767

Information

Published: May 2013
First available in Project Euclid: 29 April 2013

zbMATH: 1300.05276
MathSciNet: MR3098675
Digital Object Identifier: 10.1214/12-AOP767

Subjects:
Primary: 22F50, 37A50
Secondary: 05C05, 05C78

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 3A • May 2013
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