  Hastings first presented bounds on the second largest eigenvalue for matrices
in a Hermitian complete positive map in 2007. In this work we extend his work
to tighten these bounds. To do this, we introduce the idea of Statistically
Leinert Sets to modify the generating functions presented in Woess in 1986 and
recompute the radii of convergence in his paper in 1986. We primarily use
techniques from combinatorics and calculate norms using the ideas presented by
Akemann and Ostrang in their paper in 1976.
