A sine process is a limiting point process describing suitably rescaled bulk eigenvalues of classical Gaussian
random matrices. The 
process is the real-symmetric
limit associated with the Gaussian
orthogonal ensemble. One convention scales it to intensity 
; another uses intensity 1, related by dilation (He et
al. 2026).
He et al. (2026) reported that the local bulk eigenvalues of a uniformly random simple 
-regular graph, for every
fixed 
,
converge to 
after rescaling by the local spectral density.
