Haagerup property and group-invariant percolation

Chiranjib Mukherjee, Konstantin Recke

Let $\mathcal{G}$ be the Cayley graph of a finitely generated, infinite group $\hat{I}“$. We show that $\hat{I}“$ has the Haagerup property if and only if for every $\hat{I}\pm <1$, there is a $\hat{I}“$-inva…