  The second-order Green's function method (GF2) was shown recently to be an
accurate self-consistent approach for electronic structure of correlated
systems since the self-energy accounts for both the weak and some of the strong
correlation. The numerical scaling of GF2 is quite steep however, $O({N^5})$
(where the pre-factor is often hundreds), effectively preventing its
application to large systems. Here, we develop a stochastic approach to GF2
(sGF2) where the self-energy is evaluated by a random-vector decomposition of
Green's functions so that the dominant part of the calculation scales quasi
linearly with system size. A study of hydrogen chains shows that the resulting
approach is numerically efficient and accurate, as the stochastic errors are
very small, 0.05% of the correlation energy for large systems with only a
moderate computational effort. The method also yields automatically efficient
MP2 energies and is automatically temperature dependent.
