Free Energy Universality of Spherical Spin Glasses

TL;DR

This paper proves the universality of free energy and ground state energy in spherical spin glasses under minimal assumptions, extending previous results and resolving a conjecture for $\, ext{l}^q$ balls and tensor PCA.

Contribution

It extends universality results to spherical spin glasses with minimal moment assumptions and to $ ext{l}^q$ balls for $q>2$, resolving a conjecture and broadening applicability.

Findings

Universality of free energy and ground state energy proven for spherical spin glasses.

Extension of results to $ ext{l}^q$ balls for $q>2$.

Application of methods to tensor PCA.

Abstract

We prove the free energy and ground state energy of spherical spin glasses are universal under the minimal moment assumptions. Previously such universality was known only for Ising spin glasses and random symmetric matrices, the latter being a celebrated result of Bai--Yin. Our methods extend to $\ell^q$ balls for $q>2$, thus resolving a conjecture of Chen-Sen, and to tensor PCA.