Sampling by Intersections with Random Geodesics
From MaRDI portal
Publication:6307183
DOI10.1007/S11856-020-1979-YarXiv1809.08961MaRDI QIDQ6307183
Publication date: 24 September 2018
Abstract: In this paper we compare the different phenomena that occur when intersecting geometric objects with random geodesics on the unit sphere and inside convex bodies. On the high dimensional sphere we see that with probability bounded away from zero, the observed length will deviate from the actual measure by at most a fixed error for any subset, while in convex bodies we can always choose a subset for which the behavior would be close to a zero-one law, as the dimension grows. The result for the sphere is based on an analysis of the Radon transform. Using similar tools we analyze the variance of intersections on the sphere by higher dimensional random subspaces, and on the discrete torus by random arithmetic progressions.
Numerical approximation and computational geometry (primarily algorithms) (65Dxx) Approximations and expansions (41Axx) General and miscellaneous specific topics (00Axx) Tables in numerical analysis (65Axx)
This page was built for publication: Sampling by Intersections with Random Geodesics
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6307183)
