Edge universality of random regular graphs of growing degrees
Abstract
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.
Fields of Study & Subjects
Graph theory and applications
Spectral Theory in Mathematical Physics
Limits and Structures in Graph Theory
Publication details
- Journal / source
- The Annals of Probability
- Publisher
- Institute of Mathematical Statistics
- Volume
- 54
- Issue
- 5
- Pages
- 2377–2435
- Publication date
- 28 August 2026
- Language
- EN