Spectrum of SYK model

TL;DR

This paper rigorously proves the almost sure convergence of the eigenvalue density in the SYK model, a simplified black hole model, and discusses its largest eigenvalue.

Contribution

It provides the first rigorous proof of eigenvalue density convergence and analyzes the largest eigenvalue in the SYK model.

Findings

Eigenvalue density converges almost surely

Largest eigenvalue behavior analyzed

Foundations for spectral properties of SYK model

Abstract

This is the first part of a series of papers on the spectrum of the SYK model, which is a simple model of the black hole in physics literature. In this paper, we will give a rigorous proof of the almost sure convergence of the global density of the eigenvalues. We also discuss the largest eigenvalue of the SYK model.