We consider a sequence of Gaussian random fields that are growing tensor products of generalized Anderson–Darling processes with a given sequence of main parameters \((\mu _j)_{j\in \mathbb {N}}\) that characterize a proximity to the Gaussian white noise. The average case approximation complexity for a given d-parametric random field is defined as the minimal number of values of continuous linear functionals that is needed to approximate the field with relative 2-average error not exceeding a given threshold \(\varepsilon \) . In the paper, we obtain logarithmic asymptotics of the average case approximation complexity for such random fields with fixed \(\varepsilon \in (0,1)\) and \(d\rightarrow \infty \) for the in fact homogeneous case \(\mu _j\rightarrow c\) , \(j\rightarrow \infty \) , where \(c\in (0,\infty )\) is a constant, and for the case \(\mu _j\rightarrow \infty \) , \(j\rightarrow \infty \) , that is rather nonstandard for the practice of similar approximation problems. Bibliography: 18 titles.
