Title: Spectral Approximation for Ergodic CMV Operators with an Application to Quantum Walks,
Abstract: We establish concrete criteria for fully supported absolutely continuous
spectrum for ergodic CMV matrices and purely absolutely continuous spectrum for
limit-periodic CMV matrices. We proceed by proving several variational
estimates on the measure of the spectrum and the vanishing set of the Lyapunov
exponent for CMV matrices, which represent CMV analogues of results obtained
for Schrödinger operators due to Y.\ Last in the early 1990s. Having done so,
we combine those estimates with results from inverse spectral theory to obtain
purely absolutely continuous spectrum.