Spectral properties of distance matrices

Abstract

Distance matrices are matrices whose elements are the relative distances between points located on a certain manifold. In all cases considered here all their eigenvalues except one are non-positive. When the points are uncorrelated and randomly distributed we investigate the average density of their eigenvalues and the structure of their eigenfunctions. The spectrum exhibits delocalized and strongly localized states which possess different power-law average behaviour. The exponents depend only on the dimensionality of the manifold.

arXiv comment31 pages, 9 figures

References in corpus (2)

• Spectra of Euclidean Random Matrices
• Distance matrices, random metrics and Urysohn space

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