A deterministic Floquet circuit with a dual-unitary bulk exactly reproduces random-circuit higher-order OTOC dynamics, yielding analytic free cumulants that match full eigenstate thermalization hypothesis predictions.
Three lectures on free probability
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abstract
These are notes from a three-lecture mini-course on free probability given at MSRI in the Fall of 2010 and repeated a year later at Harvard. The lectures were aimed at mathematicians and mathematical physicists working in combinatorics, probability, and random matrix theory. The first lecture was a staged rediscovery of free independence from first principles, the second dealt with the additive calculus of free random variables, and the third focused on random matrix models.
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Free Cumulants and Full Eigenstate Thermalization from Boundary Scrambling
A deterministic Floquet circuit with a dual-unitary bulk exactly reproduces random-circuit higher-order OTOC dynamics, yielding analytic free cumulants that match full eigenstate thermalization hypothesis predictions.