Linear scaling electronic structure calculations and accurate sampling with noisy forces, has two intriguing ideas.
They compute electronic structure using a new linear scaling method that involves sampling, and thus results in noisy forces. Those forces are used to drive a molecular dynamics simulation of the nuclei (note that one of the authors is Parrinello).
For the electronic structure part of the problem, they replace a determinant in the independent particle grand potential with an integral over some fields. These fields can be sampled using a Langevin equation. This Langevin equation apparently involves only matrix-vector multiplication with a sparse matrix, which delivers the scaling.
The second part (starting in the paragraph before equation 11) is how to deal with the noisy forces in molecular dynamics. Their solution for this is to again use a Langevin equation, and to choose the size of the damping terms to cancel out the noise on average. In this way they obtain correct sampling of the Boltzmann distribution.