Norms of random matrices and widths of finite-dimensional sets

Precise orders are given for the Kolmogorov and linear widths of the unit ball of the space $l_p^m$ in the metric of $l_q^m$ for $q<\infty$. The determination of the upper estimates is based on approximation by random objects. This method goes back to Kashin (Izv. Akad. Nauk SSSR, Ser. Mat., 1977, vol. 41, p. 334–351). The corresponding lower estimates were obtained in a previous article of the author (Vestn. Leningr. Univ., 1981, № 13, p. 5–10).
Bibliography: 12 titles.