3 problems

Let $G$ and $H$ be finitely generated groups, and write $\operatorname{pdim}(G)$, $\nu\dim(G)$, and ${}^{e}\operatorname{pdim}(G)$ for the three percolation-dimension notions intro…

Let $G$ be a finitely generated group of super-polynomial growth, and let ${}^{e}\operatorname{pdim}(G)$ denote its exponential percolation dimension. Positive-dimension conjecture…

Let $G$ be a finitely generated group, and let ${}^{e}\operatorname{pdim}(G)$ denote its exponential percolation dimension. Gap conjecture. There is a $\beta>0$ such that … for eve…