Distribution of eigenvalues of large Euclidean matrices generated from lp ellipsoid

Xingyuan Zeng

Statistics & Probability Letters, 2014, vol. 91, issue C, 181-191

Abstract: 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.

Keywords: Random matrix; lp ellipsoid; lp-norm uniform distributions; Large Euclidean matrix; Empirical distributions of eigenvalues (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spl.2014.04.017

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