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We establish the absolute continuity of the integrated density of states(IDS) for quasi-periodic Schr\"odinger operators with a large trigonometricpotential and Diophantine frequency. This partially solves Eliasson's openproblem in 2002. Furthermore, this result can be extended to a class ofquasi-periodic long-range operators on $\ell^2(\Z^d)$. Our proof is based onstratified quantitative almost reducibility results of dual cocycles.Specifically, we prove that a generic analytic one-parameter family ofcocycles, sufficiently close to constant coefficients, is reducible except fora zero Hausdorff dimension set of parameters. This result affirms Eliasson'sconjecture in 2017.

Absolute continuity of the integrated density of states in the localized regime