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2013 On Euclidean random matrices in high dimension
Charles Bordenave
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Electron. Commun. Probab. 18: 1-8 (2013). DOI: 10.1214/ECP.v18-2340

Abstract

In this note, we study the n x n random Euclidean matrix whose entry (i,j) is equal to f (|| Xi - Xj ||) for some function f and the Xi's are i.i.d. isotropic vectors in Rp. In the regime where n and p both grow to infinity and are proportional, we give some sufficient conditions for the empirical distribution of the eigenvalues to converge weakly. We illustrate our result on log-concave random vectors.

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Charles Bordenave. "On Euclidean random matrices in high dimension." Electron. Commun. Probab. 18 1 - 8, 2013. https://doi.org/10.1214/ECP.v18-2340

Information

Accepted: 5 April 2013; Published: 2013
First available in Project Euclid: 7 June 2016

zbMATH: 1308.60014
MathSciNet: MR3044473
Digital Object Identifier: 10.1214/ECP.v18-2340

Subjects:
Primary: 60B20
Secondary: 15A18‎

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