  Multiple scale homogenization problems are reduced to single scale problems
in higher dimension. It is shown that sparse tensor product Finite Element
Methods (FEM) allow the numerical solution in complexity independent of the
dimension and of the length scale. Problems with stochastic input data are
reformulated as high dimensional deterministic problems for the statistical
moments of the random solution. Sparse tensor product FEM give a deterministic
solution algorithm of log-linear complexity for statistical moments.
