A non-Hermitian tridiagonal beta-ensemble is claimed to have a rotationally invariant logarithmic spectral density on a disc, but the proof's central independence lemma is false.
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Logarithmic Spectral Distribution of a Non-Hermitian $\beta$-Ensemble
A non-Hermitian tridiagonal beta-ensemble is claimed to have a rotationally invariant logarithmic spectral density on a disc, but the proof's central independence lemma is false.