A note on the large random inner-product kernel matrices

Xingyuan Zeng

Statistics & Probability Letters, 2015, vol. 99, issue C, 192-201

Abstract: In this note we consider the n×n random matrices whose (i,j)th entry is f(xiTxj), where xi’s are i.i.d. random vectors in RN, and f is a real-valued function. The empirical spectral distributions of these random inner-product kernel matrices are studied in two kinds of high-dimensional regimes: n/N→γ∈(0,∞) and n/N→0 as both n and N go to infinity. We obtain the limiting spectral distributions for those matrices from different random vectors in RN including the points lp-norm uniformly distributed over four manifolds. And we also show a result on isotropic and log-concave distributed random vectors, which confirms a conjecture by Do and Vu.

Keywords: Random inner-product kernel matrix; Empirical spectral distribution; High dimension; Four manifolds; Log-concave (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715215000206
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:99:y:2015:i:c:p:192-201

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2015.01.014

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().