Isoperimetric lower bounds for critical exponents for long-range percolation

Johannes Bäumler, Noam Berger

We study independent long-range percolation on ${\mathbb{Z}}^d$ where the vertices $x$ and $y$ are connected with probability $1-e^{-\beta \Vert x-y{\Vert }^{-d-\alpha }}$ for $\alpha >0$. Provided the critic…