We show that a generic element of a space of limit-periodic CMV operators haszero-measure Cantor spectrum. We also prove a Craig--Simon type theorem for thedensity of states measure associated with a stochastic family of CMV matricesand use our construction from the first part to prove that the Craig--Simonresult is optimal in general. We discuss applications of these results to aquantum walk model where the coins are arranged according to a limit-periodicsequence. The key ingredient in these results is a new formula which may beviewed as a relationship between the density of states measure of a CMV matrixand its Schur function.
展开▼
