# Kesten-McKay law for random subensembles of Paley equiangular tight frames

## TL;DR

This paper proves a conjecture about the singular value distribution of random subensembles of Paley equiangular tight frames using the method of moments, with potential for broader applications.

## Contribution

It introduces a novel proof of a conjecture on singular value distribution for Paley equiangular tight frames and extends the analysis to more general real equiangular tight frames.

## Key findings

- Confirmed the conjecture for Paley equiangular tight frames
- Extended analysis to real equiangular tight frames of redundancy 2
- Suggests potential for broader generalizations in frame theory

## Abstract

We apply the method of moments to prove a recent conjecture of Haikin, Zamir and Gavish (2017) concerning the distribution of the singular values of random subensembles of Paley equiangular tight frames. Our analysis applies more generally to real equiangular tight frames of redundancy 2, and we suspect similar ideas will eventually produce more general results for arbitrary choices of redundancy.