4 problems

Let $G$ be a Cayley graph of a non-amenable group, or more generally a quasi-transitive graph with positive Cheeger constant. For Bernoulli percolation on $G$, let $p_c$ be the cri…

Let $\Gamma$ be a finitely generated group and let $S$ be a finite generating set. Write $\rho(\Gamma,S)$ for the spectral radius of the associated Cayley graph. Spectral-radius co…

The preceding discussion concerns actions of countable groups that are essentially free, weakly mixing, probability-measure-preserving, amenable, of type $III_\lambda$, and of stab…

Let $G$ be the group of rigid motions, let $\widehat G_r=\widehat G_p\cup\widehat G_d$ be its restricted dual, with principal series $\widehat G_p$ and discrete series…