2019/06/09 by Zakhar Kabluchko, Joscha Prochno, Kabluchko, Zakhar +3
Mathematics · #46B09 #52A23 Secondary: 60D05 #FOS: Mathematics #Functional Analysis (math.FA) #Geometry and complex manifolds #Metric Geometry (math.MG) #Point processes and geometric inequalities #Primary: 60F10 #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1906.03599
openalex publication_date 2019/06/09 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
In this article we prove three fundamental types of limit theorems for the q-norm of random vectors chosen at random in an ℓpn-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 non-random projections of ℓpn-balls to lower-dimensional subspaces are discussed as well. The text is a continuation of [Kabluchko, Prochno, Thäle: High-dimensional limit theorems for random vectors in ℓpn-balls, Commun. Contemp. Math. (2019)].