Absolutely Continuous Convolutions of Singular Measures and an Application to the Square Fibonacci Hamiltonian

Abstract

We prove for the square Fibonacci Hamiltonian that the density of states measure is absolutely continuous for almost all pairs of small coupling constants. This is obtained from a new result we establish about the absolute continuity of convolutions of measures arising in hyperbolic dynamics with exact-dimensional measures.Comment: 28 pages, to appear in Duke Math.