Diameters of random Cayley graphs of finite nilpotent groups

Abstract We prove the existence of a limiting distribution for appropriately rescaled diameters random undirected Cayley graphs finite nilpotent groups bounded rank and nilpotency class, thus extending result Shapira Zuck which dealt with case abelian groups. The is defined on space unimodular lattices, as in Our result, when specialised to certain family unitriangular groups, establishes very recent conjecture Hermon Thomas. derive this consequence general inequality, showing that diameter graph group governed by its abelianisation.