  We consider an \eps-approximation by n-term partial sums of the
Karhunen-Lo\`eve expansion to d-parametric random fields of tensor product-type
in the average case setting. We investigate the behavior, as d tends to
infinity, of the information complexity n(\eps,d) of approximation with error
not exceeding a given level \eps. It was recently shown by M.A. Lifshits and
E.V. Tulyakova that for this problem one observes the curse of dimensionality
(intractability) phenomenon. The aim of this paper is to give the exact
asymptotic expression for the information complexity n(\eps,d).
