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We study the spectral properties of a class of random matrices where thematrix elements depend exponentially on the distance between uniformly andrandomly distributed points. This model arises naturally in various physicalcontexts, such as the diffusion of particles, slow relaxations in glasses, andscalar phonon localization. Using a combination of a renormalization groupprocedure and a direct moment calculation, we find the eigenvalue distributiondensity (i.e., the spectrum) and the localization properties of the eigenmodes,for arbitrary dimension. Finally, we discuss the physical implications of theresults.

Localization, anomalous diffusion and slow relaxations: a random distance matrix approach