Distribution of eigenvalues of large Euclidean matrices generated from lplp ellipsoid

In this paper, we study large Euclidean random matrices Mn=(fn(‖xi−xj‖2))n×n where xi’s are i.i.d. points lplp-norm uniformly distributed over the NN dimensional lplp ellipsoid or its surface, fnfn is a real function on [0,∞)[0,∞) and ‖⋅‖‖⋅‖ is the Euclidean distance. Under the assumption that both NN and nn go to infinity proportionally, we obtain the limiting empirical distribution of the eigenvalues of Mn. The limit is closely related to the semi-axis lengths of the lplp ellipsoid or its surface.