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