Spectrum of SYK model II: Central limit theorem

TL;DR

This paper proves the central limit theorem for eigenvalue linear statistics in the SYK model, extending previous work on eigenvalue density convergence to include fluctuation analysis.

Contribution

It establishes the CLT for eigenvalue linear statistics in the SYK model and computes the variance, advancing understanding of spectral fluctuations.

Findings

Proves the CLT for eigenvalue linear statistics in the SYK model.

Calculates the variance of the eigenvalue linear statistics.

Extends previous results on eigenvalue density convergence.

Abstract

In our previous paper \cite{FTD1}, we derived the almost sure convergence of the global density of eigenvalues of random matrices of the SYK model. In this paper, we will prove the central limit theorem for the linear statistic of eigenvalues and compute its variance.