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In this paper, we study the probability distribution of eigenvalues of theEuclidean random matrix whoseentry is of the formfor some real function  f . Random points's are independently distributed in theellipsoid or on its surface inincluding the unit sphere, the simplex, the ordinary ellipsoid and the hyper-cube. Hereis allowed to be any real number which includes the two most interesting casesand. The limits of the empirical distribution of its eigenvalues are derived in two high dimensional settings:andas both  n  and  N  go to infinity. By takingto be suitable functions, we also give the explicit limiting spectral distributions for some distance matrices whose entries are based on the Euclidean distance and the geodesic distance.

Spectrum of large euclidean random matrices generated from l p ellipsoids