Appetizer Using Probability to Cover a Set
Abstract
This chapter begins with Maurey’s empirical method – a probabilistic approach to constructing economical convex combinations. We apply it to bound covering numbers and the volumes of polytopes, revealing their counterintuitive behavior in high dimensions. The exercises refine these bounds and culminate in the Carl–Pajor theorem on the volume of polytopes.
Fields of Study & Subjects
Point processes and geometric inequalities
Advanced Banach Space Theory
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- Cambridge University Press eBooks
- Pages
- 1–7
- Publication date
- 30 January 2026
- Document type
- Book chapter