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Spectral properties of distance matrices

2003/01/29 by E. Bogomolny, O. Bohigas, C. Schmit · 1 citation
Physics and Astronomy · #nlin.CD

paper · pdf · doi:10.1088/0305-4470/36/12/341

published as J. Phys. A: Math. Gen. 36 (2003) · 31 pages, 9 figures

arxiv created 2003/01/29 · arxiv updated 2009/11/30

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.

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