LOE for Haar random dynamics asymptotically matches the Page curve for traceless operators and is independent of the initial operator at leading order.
Voiculescu, Limit laws for random matrices and free products, Inventiones mathematicae104, 201–220 (1991)
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Page Curve for Local-Operator Entanglement from Free Probability
LOE for Haar random dynamics asymptotically matches the Page curve for traceless operators and is independent of the initial operator at leading order.