Invariant Monotone Coupling Need Not Exist

Details Invariant Monotone Coupling Need Not Exist Invariant Monotone Coupling Need Not Exist

2010-11-10

arxiv.org/abs/1011.2283v1

Mathematics

Probability

10 pages

Scientific paper

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

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