Fixed Price of Groups and Percolation

Abstract

We prove that for every finitely generated group $\Gamma$, at least one of the following holds: (1) $\Gamma$ has fixed price; (2) each of its Cayley graphs $G$ has infinitely many infinite clusters for some Bernoulli percolation on $G$.

3 pp

Cited by in corpus (1)

• Small spectral radius and percolation constants on non-amenable Cayley graphs