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Spectral properties of distance matrices

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arxiv nlin/0301044 v1 pith:ZARRDLDO submitted 2003-01-29 nlin.CD

classification nlin.CD
keywords matricesaveragedistanceeigenvaluesmanifoldpointsbehaviourcases
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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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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions

    cs.LG 2026-06 unverdicted novelty 7.0 of 10

    Observable Matrix Dynamics (OMD) is a new diagnostic framework that uses random matrix theory on distance matrices to distinguish diffusive relaxations from phase-transition-like reorganizations during neural network ...

  2. Are Three Matrices All You Need To Beat the Market? Observable Matrix Dynamics for Portfolio Optimization

    q-fin.PM 2026-07 conditional novelty 6.0 of 10

    A three-matrix, rank-based Markov-chain portfolio reports out-of-sample Sharpes of 1.06 and 1.32 vs the market's 0.78 and 1.14, net of costs, even though its return rank is itself 'close to unforecastable.'

  3. Observable Matrix Dynamics of Stocks

    q-fin.ST 2026-07 conditional novelty 6.0 of 10

    Applying the Observable Matrix Dynamics toolkit to S&P 500 data yields crisis-specific correlation geometries, a market that never settles into a stable structure, and a weak episodic time-asymmetry in the volatility ranking.

  4. I-BBS: Coordinate-Free Inference of Latent Sub-Manifolds Using Random Distance Matrix Theory

    cs.LG 2026-06 unverdicted novelty 6.0 of 10

    I-BBS recovers latent manifold dimension d and geometry from ambient distance matrices via two noise-stable integer signatures: top non-Perron multiplet multiplicity and a parameter-free shrinkage law.

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