Hölder regularity of integrated density of states for the almost Mathieu operator in a perturbative regime (Q1580923)

When an almost Mathieu operator on the lattice is considered, the author shows that in the limit, the integrated density of states is Hölder continuous for a certain exponent range. He shows that this result is similar to the one obtained in a perturbative regime for a one-dimensional quasiperiodic lattice of Schrödinger operators with an assumed positive Lyapunov exponent. The latest approach also provides a new way to control Green's functions.