Continuity of the critical value and a shape theorem for long-range percolation

Johannes Bäumler

Consider supercritical long-range percolation on ${\mathbb{Z}}^d$ where two vertices $x,y\in {\mathbb{Z}}^d$ are connected with probability asymptotic to $\Vert x-y{\Vert }^{-s}$ for some $s>2d$. Conditioned t…