A factor of i.i.d with uniform marginals and infinite clusters spanned by equal labels

Abstract

We give an example of an $\mathsf{FIID}$ vertex-labeling of ${\mathbb{T}}_3$ whose marginals are uniform on $[0,1]$, and if we delete the edges between those vertices whose labels are different, then some of the remaining clusters are infinite.

arXiv comment9 pages. The exposition has been changed substantially