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

## TL;DR

This paper provides a rigorous theoretical foundation for a variance reduction method in the computation of material properties of random alloys within the Thomas-Fermi-von Weizs"acker model, extending locality results to include point charges.

## Contribution

It offers a rigorous justification for a variance reduction technique in the TFW model, incorporating an extension of exponential locality to point charges.

## Key findings

- Rigorous justification of a variance reduction method in the TFW model.
- Extension of exponential locality results to include point charges.
- Potential implications for more accurate simulations of random alloys.

## Abstract

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