Bounds on the density of states of random Schrödinger operators

Bounds are obtained on the unintegrated density of states ρ(E) of random Schrödinger operators H=-Δ + V acting on L²(ℝ^d) or l²(ℤ^d). In both cases the random potential is {Mathematical expression}in which the {Mathematical expression} are IID random variables with density f. The χ denotes indicator function, and in the continuum case the {Mathematical expression} are cells of unit dimensions centered on y∈ℤ^d. In the finite-difference case Λ(y) denotes the site y∈ℤ^d itself. Under the assumption f ∈ L₀^1+e{open}(ℝ) it is proven that in the finitedifference case p ∈ L^∞(ℝ), and that in the d= 1 continuum case p ∈ L_loc^∞(ℝ).