Spectral properties of distance matrices
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Publication:4443918
DOI10.1088/0305-4470/36/12/341zbMATH Open1057.15027arXivnlin/0301044OpenAlexW2129923964WikidataQ56779545 ScholiaQ56779545MaRDI QIDQ4443918
E. B. Bogomolny, Oriol Bohigas, Charles Schmit
Publication date: 19 January 2004
Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/nlin/0301044
Central limit and other weak theorems (60F05) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52)
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