Resumen de Locality of percolation for Abelian Cayley graphs

Sébastien Martineau, Vincent Tassion

• We prove that the value of the critical probability for percolation on an Abelian Cayley graph is determined by its local structure. This is a partial positive answer to a conjecture of Schramm: the function pcpc defined on the set of Cayley graphs of Abelian groups of rank at least 22 is continuous for the Benjamini–Schramm topology. The proof involves group-theoretic tools and a new block argument.