Locality of percolation for abelian Cayley graphs

We show that the value of the critical parameter of percolation depends essentially only on the local structure of the abelian Cayley graph under consideration. More precisely, we prove that the function mapping any graph to its critical point is continuous for the local topology in restriction to the abelian Cayley graphs satisfying \(p_c<1\).

Annals of Probability, 45(2):1247–1277, 2017

Six years later, with Daniel Contreras, we generalised this result to homogeneous graphs with polynomial growth.