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Article Dans Une Revue Electronic Communications in Probability Année : 2013

On Euclidean random matrices in high dimension

Résumé

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.

Dates et versions

hal-00948726 , version 1 (18-02-2014)

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Charles Bordenave. On Euclidean random matrices in high dimension. Electronic Communications in Probability, 2013, 18, pp.1-8. ⟨10.1214/ECP.v18-2340⟩. ⟨hal-00948726⟩
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