  Eigenvalue distributions of properly regularized Wilson loop operators are
used to study the transition from ultra-violet (UV) behavior to infra-red (IR)
behavior in gauge theories coupled to matter that potentially have an IR fixed
point (FP). We numerically demonstrate emergence of scale invariance in a
matrix model that describes $SU(N)$ gauge theory coupled to two flavors of
massless adjoint fermions in the large $N$ limit. The eigenvalue distribution
of Wilson loops of varying sizes cannot be described by a universal lattice
beta-function connecting the UV to the IR.
