Spectrum of multispace Euclidean random matrices

Aldo Battista (1, 2) , Remi Monasson (2)

1 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]
2 Physique Statistique et Inférence pour la Biologie

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.

Domaines: Systèmes désordonnés et réseaux de neurones [cond-mat.dis-nn]; Mécanique statistique [cond-mat.stat-mech]

Aldo Battista, Remi Monasson. Spectrum of multispace Euclidean random matrices. Physical Review E , 2020, 101 (5), ⟨10.1103/physreve.101.052133⟩. ⟨hal-02508767v2⟩