Distribution of eigenvalues of large Euclidean matrices generated from lp 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 lp-norm uniformly distributed over the N dimensional lp ellipsoid or its surface, fn is a real function on [0,∞) and ‖⋅‖ is the Euclidean distance. Under the assumption that both N and n 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 lp ellipsoid or its surface.