In the large N limit, singular values of randomly twisted transfer operators obey a Weyl law almost surely with rapid decay, and extending the polynomial method to infinite dimensions yields a smooth probabilistic version.
Tropp, and Ramon van Handel
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Randomly twisted transfer operators and singular values statistics
In the large N limit, singular values of randomly twisted transfer operators obey a Weyl law almost surely with rapid decay, and extending the polynomial method to infinite dimensions yields a smooth probabilistic version.