  Using numerical methods for finding Ricci-flat metrics, we explore the
spectrum of local operators in two-dimensional conformal field theories defined
by sigma models on Calabi-Yau targets at large volume. Focusing on the examples
of K3 and the quintic, we show that the spectrum, averaged over a region in
complex structure moduli space, possesses the same statistical properties as
the Gaussian orthogonal ensemble of random matrix theory.
