On Euclidean random matrices in high dimension

Charles Bordenave (Université de Toulouse & CNRS)


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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Pages: 1-8

Publication Date: April 5, 2013

DOI: 10.1214/ECP.v18-2340


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