Weighted isoperimetry implies percolation

Ivailo Hartarsky, Franco Severo, Augusto Teixeira

Consider an infinite edge-weighted graph satisfying an isoperimetric inequality of the type $\Vert \partial A\Vert \ge C|A{|}^{\alpha }$ for some $\alpha ,C>0$, where $\Vert \partial A\Vert$ denotes the weighte…