ON THE DISTRIBUTION OF IWASAWA INVARIANTS ASSOCIATED TO MULTIGRAPHS

Source abstract

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.