Perturbative diagonalisation for Maryland-type quasiperiodic operators with flat pieces

Abstract: We consider quasiperiodic operators on $\mathbb Z^d$ with unbounded monotone sampling functions ("Maryland-type"), which are not required to be strictly monotone and are allowed to have flat segments. Under several geometric conditions on the frequencies, lengths of the segments, and their positions, we show that these operators enjoy Anderson localization at large disorder.