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arXiv · 1011.2283

Invariant monotone coupling need not exist

Péter Mester
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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. 2010-11-10. Invariant monotone coupling need not exist. https://doi.org/10.1214/12-aop767

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