Haagerup property and group-invariant percolation

Chiranjib Mukherjee, Konstantin Recke

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