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Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian

Published Web Location

https://doi.org/10.1215/00127094-3119739
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.

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