Compressions and isoperimetric inequalities

AbstractThe main aim of this paper is to prove that, for a connected graph G, the sequence (Gn)1∞ of powers of G is a normal Lévy family, and to obtain a good constant in the exponent. Our proof is based on a best possible isoperimetric inequality in grid graphs, that is, products of paths. In order to prove this inequality, we introduce some generalised compression operators