  We report a linear-scaling random Green's function (rGF) method for
large-scale electronic structure calculation. In this method, the rGF is
defined on a set of random states to stochastically express the density matrix,
and rGF is calculated with the linear-scaling computational cost. We show the
rGF method is generally applicable to the nonorthogonal localized basis, and
circumvent the large Chebyshev expansion for the density matrix. As a
demonstration, we implement rGF with density-functional Tight-Binding method
and apply it to self-consistently calculate water clusters up 9984 H2Os. We
find the rGF method combining with a simple fragment correction can reach an
error of ~1meV per H2O in total energy, compared to the deterministic
calculations, due to the self-average. The development of rGF method advances
the stochastic electronic structure theory to a new stage of the efficiency and
applicability.
