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In the computation of the material properties of random alloys, the method of"special quasirandom structures" attempts to approximate the properties of thealloy on a finite volume with higher accuracy by replicating certain statisticsof the random atomic lattice in the finite volume as accurately as possible. Inthe present work, we provide a rigorous justification for a variant of thismethod in the framework of the Thomas-Fermi-von Weizs\"acker (TFW) model. Ourapproach is based on a recent analysis of a related variance reduction methodin stochastic homogenization of linear elliptic PDEs and the localityproperties of the TFW model. Concerning the latter, we extend an exponentiallocality result by Nazar and Ortner to include point charges, a result that maybe of independent interest.

Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizs\"acker model