Spectrum of SYK model

Renjie Feng, Gang Tian, Dongyi Wei

Published 2018-01-30Version 1

We will study the spectral properties of the random matrix of SYK model, which is a simple model of the black hole in physics literature. Our primary interest is the distribution of the eigenvalues as the number of Majorana fermions tends to infinity. We will first prove the almost surely convergence of the global density of the eigenvalues. Then we show that the linear statistics of the eigenvalues satisfy the central limit theorem asymptotically. In the last section, we also discuss the largest eigenvalue of the SYK model.