  We propose a method for the approximation of solutions of PDEs with
stochastic coefficients based on the direct, i.e., non-adapted, sampling of
solutions. This sampling can be done by using any legacy code for the
deterministic problem as a black box. The method converges in probability (with
probabilistic error bounds) as a consequence of sparsity and a concentration of
measure phenomenon on the empirical correlation between samples. We show that
the method is well suited for truly high-dimensional problems (with slow decay
in the spectrum).
