Borel summability in the disorder parameter of the averaged Green's function for Gaussian disorder

In this note we prove Borel summability in the disorder parameter of the averaged Green's function <G(E,x,y>) _y of tight binding models $$H_V = - Delta + V$$ with Gaussian disorder $$dlambda (V) = (2pi gamma )^{ - 1/2} exp ( - V^2 /2gamma )dV$$ forγ→0 and fixed large |E|. Using this, we can reconstruct the density of states ?(E)γ from the Borel sums of <G(E,x,x>) _y with ImE↗0 and ImE↘0.