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We study Anderson and alloy type random Schr\"odinger operators on$\ell^2(\ZZ^d)$ and $L^2(\RR^d)$. Wegner estimates are bounds on the averagenumber of eigenvalues in an energy interval of finite box restrictions of thesetypes of operators. For a certain class of models we prove a Wegner estimatewhich is linear in the volume of the box and the length of the consideredenergy interval. The single site potential of the Anderson/alloy type modeldoes not need to have fixed sign, but it needs be of a generalised stepfunction form. The result implies the Lipschitz continuity of the integrateddensity of states.

Wegner estimates for sign-changing single site potentials