Classic Proofs

On this page I have presented several classical proofs in percolation theory.

All proofs here will be before 2000!!

Aizenmann-Barsky proof of sharpness

Employing techniques from differential inequalities and the so-called ghost field we present the famous theorem on subcritical sharpness. The article can be found [here]

Aizenmann-Kesten-Newman proof for uniqueness of infinite cluster

Nowadays, the Burton-Keane argument often overshadows the AKN proof for uniqueness of infinite cluster, in the below article we present their proof while giving an extension to the amenable case. The article can be found [here].