Probabilistic and average widths of multivariate Sobolev spaces with mixed derivative equipped with the Gaussian measure (Q706793)

Let \({\mathbb T}=[0,\,2\pi)\) be the torus. \textit{V. E. Maiorov} [Russ. Acad. Sci., Sb. Math. 79, 265--279 (1994; Zbl 0828.41011)] studied the probabilistic \((N,\delta)\)-width and \(p\)-average \(N\)-width of the univariate Sobolev space \(W_2^r({\mathbb T})\) with Gaussian measure. In this paper, the results of V. E. Maiorov are extended to the multivariate case. The authors determine the asymptotic order of the probabilistic \((N,\delta)\)-width and \(p\)-average width of the multivariate Sobolev space with mixed derivative, equipped with a Gaussian measure in \(L_q({\mathbb T}^d)\) \((1<q<\infty)\).