For every fixed degree d≥3, sufficiently weak fixed positive uniform diagonal disorder on a uniformly random simple d-regular graph yields the GOE bulk microscopic eigenvalue point process at each fixed energy separated from the clean spectral edges, after rescaling by the corresponding tree density of states.
For every fixed degree d≥3, sufficiently weak fixed positive uniform diagonal disorder on a uniformly random simple d-regular graph yields the GOE bulk microscopic eigenvalue point process at each fixed energy separated from the clean spectral edges, after rescaling by the corresponding tree density of states.
For every fixed degree d≥3, sufficiently weak fixed positive uniform diagonal disorder on a uniformly random simple d-regular graph yields the GOE bulk microscopic eigenvalue point process at each fixed energy separated from the clean spectral edges, after rescaling by the corresponding tree density of states.
If correct, extends fixed-energy GOE bulk universality to positive weak Anderson disorder at every fixed regular degree.
Do weakly disordered fixed-degree random regular graphs have GOE statistics at a fixed bulk energy?
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OpenAI reports fixed-energy GOE statistics for weakly disordered regular graphs
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