Grassmann angles of infinite-dimensional cones

M. K. Dospolova

Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 34, Tome 525 (2023), pp. 51-70

Résumé

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.

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