Moments of Subsets of General Equiangular Tight Frames

Abstract

This note outlines the steps for proving that the moments of a randomly-selected subset of a general ETF (complex, with aspect ratio $0<\gamma <1$) converge to the corresponding MANOVA moments. We bring here an extension for the proof of the 'Kesten-Mckay' moments (real ETF, $\gamma =1/2$) \cite{magsino2020kesten}. In particular, we establish a recursive computation of the $r$th moment, for $r=1,2,\dots$, and verify, using a symbolic program, that the recursion output coincides with the MANOVA moments.