On Euclidean random matrices in high dimension
نویسنده
چکیده
In this note, we study the n×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 inR. 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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