On the distribution of Iwasawa invariants associated to multigraphs

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