Random points in the unit ball of \(\ell^{ n }_{ p }\)
type: Item
instance of: scholarly article
title: Random points in the unit ball of \(\ell^{ n }_{ p }\)
zbMATH Open document ID: 1116.15018
author: G. Aubrun
published in: Positivity
publication date: 2007-02-13T00:00:00Z
review text: Two well-known results in random matrix theory are due to \textit{V. A. Marčenko} and \textit{L. A. Pastur} [Math. USSR, Sb. 1, 457--483 (1967; Zbl 0162.22501)], and \textit{Z. D. Bai} and \textit{Y. Q. Yin} [Ann. Probab. 21, No. 3, 1275--1294 (1993; Zbl 0779.60026)]. In the paper under review, the author proves analogs of those theorems, in the case where the condition ``identically distributed independent entries'' is replaced by ``uniformly distributed (on a certain ball of \(\ell_n^p\)) independent rows''.
reviewed by: Martín Argerami
Mathematics Subject Classification ID: 15B52
Mathematics Subject Classification ID: 52A21
zbMATH DE Number: 5125392
zbMATH Keywords: \(\ell^n_p\) spaces
zbMATH Keywords: random matrices
zbMATH Keywords: random vectors
zbMATH Keywords: uniformly distributed independent rows
MaRDI profile type: Publication
full work available at URL: s11117-005-0039-5
OpenAlex ID: W2103078728
cites work: Sampling convex bodies: a random matrix approach
cites work: Limit of the smallest eigenvalue of a large dimensional sample covariance matrix
cites work: A probabilistic approach to the geometry of the \(\ell^n_p\)-ball
cites work: Q4269108
DOI: 10.1007/S11117-005-0039-5
description: scientific article; zbMATH DE number 5125392