The Wegner estimate and the integrated density of states for some random operators

Dynamical delocalization in random Landau Hamiltonians

“…Although the Wegner estimate does not follow from Hölder continuity of the integrated density of states, we use some of the key results in [CoHKR] to obtain the crucial estimate [CoHK,Eq. (3.1)], from which the Wegner estimate follows as in [CoHK,Proof of Theorem 1.2].…”

H�lder Equicontinuity of the Integrated Density of States at Weak Disorder

“…However the methods employed herein are in fact quite different from those of ref. [1], and may be interesting in and of themselves.…”

“…(2) for the integrated density of states associated to a continuum random Schrödinger operator is implicit in Theorem 1.1 of ref. [1], although uniformity in λ is not explicitly noted there. The tools of ref.…”

“…The tools of ref. [1] carry over easily to the discrete context to give an alternative proof of eq. (2).…”

From Uncertainty Principles to Wegner Estimates

“…Evidently, the latter theorem was not known to Combes, Hislop and Klopp who proved a similar but somewhat different result with H 0 = −∆ + V 0 , where V 0 and W are periodic over the same lattice in [4]: Theorem 2.4. Let H 0 = −∆ + V 0 , with V 0 and W periodic over the same lattice and W = 0 on some open set.…”