A factor of i.i.d. with uniform marginals and infinite clusters spanned by equal labels
Péter Mester · Ergodic Theory and Dynamical Systems · 2022
Abstract We give an example of an 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. We also show that no such process can be finitary.