Approximation of Tensor-type Random fields

In this work (joint with E.Tulliakova and M.Zani) we consider random fields of tensor product type and more complicated additive fields. We investigate the quality of finite rank approximation (both in the average and in the probabilistic sense). Of special importance is the case when dimension of parametric set tends to infinity . We show that, for any fixed level of relative error, approximation complexity ncreases exponentially and find the explosion coefficient. Interestingly, the solution of the probabilistic problem reduces to the analysis of a deterministic array of eigenvalues while the latter is performed via the central limit theorem.