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Three lectures on free probability
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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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Cited by 3 Pith papers
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Free Probability in a Minimal Quantum Circuit Model
In a solvable random-circuit model, all higher-order OTOCs decay at the same rate λ^{2t} (λ from a single-particle channel), and their late-time values match the free-cumulant decomposition predicted by full ETH.
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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.
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Energy dynamics in a class of local random matrix Hamiltonians
Energy dynamics in a class of local random matrix Hamiltonians is exactly mapped, in a large local Hilbert space limit, to single-particle hopping on a lattice or Bethe tree.
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