Spectral properties of distance matrices

Details Spectral properties of distance matrices Spectral properties of distance matrices

2003-01-29

arxiv.org/abs/nlin/0301044v1

J. Phys. A: Math. Gen. 36 (2003)

Nonlinear Sciences

Chaotic Dynamics

31 pages, 9 figures

Scientific paper

10.1088/0305-4470/36/12/341

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.

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