On the Spectrum of Multi-Space Euclidean Random Matrices

Abstract

We consider the additive superimposition of an extensive number of independent Euclidean Random Matrices in the high-density regime. The resolvent is computed with techniques from free probability theory, as well as with the replica method of statistical physics of disordered systems. Results for the spectrum and eigenmodes are shown for a few applications relevant to computational neuroscience, and are corroborated by numerical simulations.

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Cited by in corpus (2)

• Capacity-resolution trade-off in the optimal learning of multiple low-dimensional manifolds by attractor neural networks
• Eigenvalue spectrum of neural networks with arbitrary Hebbian length