2023
DOI: 10.48550/arxiv.2301.09543
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Generic MANOVA limit theorems for products of projections

Abstract: We study the convergence of the empirical spectral distribution of ABA for N × N orthogonal projection matrices A and B, where 1 N Tr(A) and 1 N Tr(B) converge as N → ∞, to Wachter's MANOVA law. Using free probability, we show mild sufficient conditions for convergence in moments and in probability, and use this to prove a conjecture of Haikin, Zamir, and Gavish (2017) on random subsets of unit-norm tight frames. This result generalizes previous ones of Farrell (2011) andMagsino, Mixon, andParshall (2021). We … Show more

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