ON THE DISTRIBUTION OF IWASAWA INVARIANTS ASSOCIATED TO MULTIGRAPHS

Abstract

AbstractLet$\ell $be a prime number. The Iwasawa theory of multigraphs is the systematic study of growth patterns in the number of spanning trees in abelian$\ell $-towers of multigraphs. In this context, growth patterns are realized by certain analogs of Iwasawa invariants, which depend on the prime$\ell $and the abelian$\ell $-tower of multigraphs. We formulate and study statistical questions about the behavior of the Iwasawa$\mu $and$\lambda $invariants.