Grassmann angles of infinite-dimensional cones
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 34, Tome 525 (2023), pp. 51-70
Voir la notice de l'article provenant de la source Math-Net.Ru
In 1985, B. S. Tsirelson discovered a deep connection between Gaussian processes and important geometric characteristics of a convex compact sets in an infinite-dimensional separable Hilbert space, called intrinsic volumes. F. Götze, Z. Kabluchko and D. N. Zaporozhets in their recent work (2021) presented a conic version of Tsirelson's theorem for Grassmann angles of finite-dimensional cones, which are analogues of intrinsic volumes, and also proved a theorem on the connection between the Grassmann angles of a positive hull of a set and the absorption probability of the convex hull of its Gaussian image. In this paper we prove a generalizations of the latter results to the case of infinite-dimensional cones in a separable Hilbert space.
@article{ZNSL_2023_525_a4,
author = {M. K. Dospolova},
title = {Grassmann angles of infinite-dimensional cones},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {51--70},
publisher = {mathdoc},
volume = {525},
year = {2023},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2023_525_a4/}
}
M. K. Dospolova. Grassmann angles of infinite-dimensional cones. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 34, Tome 525 (2023), pp. 51-70. http://geodesic.mathdoc.fr/item/ZNSL_2023_525_a4/