Under mild dimension conditions, the empirical spectral distribution of sparse high-dimensional random geometric graphs matches the semicircle law or the Erdős-Renyi limit.
On the spectrum of dense random geometric graphs.The Annals of Applied Probability, 32(3):1734–1773, 2022
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Spectra of high-dimensional sparse random geometric graphs
Under mild dimension conditions, the empirical spectral distribution of sparse high-dimensional random geometric graphs matches the semicircle law or the Erdős-Renyi limit.