LIMIT THEOREMS FOR THE VOLUMES OF SMALL CODIMENSIONAL RANDOM SECTIONS OF-BALLS

• 成果类型: Article
• 署名作者: Adamczak, Radoslaw; Pivovarov, Peter; Simanjuntak, Paul
• 署名单位: University of Warsaw; University of Missouri System; University of Missouri Columbia
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/23-AOP1646
• 发表日期: 2024
• 页码: 93-126
• 关键词: random projections; random points; intersection bodies; random polytopes; random-variables; surface measure; vertices; inequalities; BOUNDARY; moments

摘要

We establish central limit theorems for the volumes of intersections of Bpn (the unit ball of in p) with uniform random subspaces of codimension d for fixed d and n -> infinity. As a corollary we obtain higher-order approximations for expected volumes, refining previous results by Koldobsky and Lifschitz and approximations obtained from the Eldan-Klartag version of CLT for convex bodies. We also obtain a central limit theorem for the Minkowski functional of the intersection body of Bnp, evaluated on a random vector distributed uniformly on the unit sphere.