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Wegner Estimate for Random Divergence-Type Operators Monotone in the Randomness
W ′ W and (8) with t = 1 implies
EL n (B + W ′ Id) EL
n (B) + E2−η
( βμq
4G
)N ′·(1+E 2/3 ++)
.
(ii) If p > q, then t := μp−q ∈ (0, 1) and W ′ = tW . With this choice of t
inequality (8) implies
EL n [...] a tool that was developed to prove localization for random Schrödinger operators, cf., e.g., [6, 8]. In order to start it, one needs to prove an initial length scale and a Wegner estimate. Historically [...] depending only on θE , θL,G, η and the dimension d, such that for allL ∈ GN, all δ ∈ (0, δ0], all
22 Page 8 of 14 Math Phys Anal Geom (2021) 24: 22
(G, δ)-equidistributed sequences Z, all W ∈ L∞(L) satisfying …