On the Distribution of Iwasawa Invariants Associated to Multigraphs

Abstract

Let $\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.