Highdimensional limit theorems for random vectors in $\ell_p^n$balls. II
Abstract
In this article we prove three fundamental types of limit theorems for the $q$norm of random vectors chosen at random in an $\ell_p^n$ball in high dimensions. We obtain a central limit theorem, a moderate deviations as well as a large deviations principle when the underlying distribution of the random vectors belongs to a general class introduced by Barthe, Guédon, Mendelson, and Naor. It includes the normalized volume and the cone probability measure as well as projections of these measures as special cases. Two new applications to random and nonrandom projections of $\ell_p^n$balls to lowerdimensional subspaces are discussed as well. The text is a continuation of [Kabluchko, Prochno, Thäle: Highdimensional limit theorems for random vectors in $\ell_p^n$balls, Commun. Contemp. Math. (2019)].
 Publication:

arXiv eprints
 Pub Date:
 June 2019
 arXiv:
 arXiv:1906.03599
 Bibcode:
 2019arXiv190603599K
 Keywords:

 Mathematics  Probability;
 Mathematics  Functional Analysis;
 Mathematics  Metric Geometry;
 Primary: 60F10;
 52A23 Secondary: 60D05;
 46B09