Mathematical analysis demonstrates Tracy–Widom distribution fluctuations in random regular graphs, indicating bounded nontrivial eigenvalues in most networks.
We consider the statistics of extreme eigenvalues of random d-regular graphs, with Nc≤d≤N1/3−c for arbitrarily small c>0. We prove that in this regime, the fluctuations of extreme eigenvalues are given by the Tracy–Widom distribution. As a consequence, about 69% of d-regular graphs have all nontrivial eigenvalues bounded in absolute value by 2 d−1.
No takes yet. Share an insight, caveat, or question.
Huang et al. (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: