User-Friendly Tools for Random Matrices II

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" summary

Proves a concrete tail bound for a matrix Rademacher series: P(λ_max(X) ≥ t) ≤ D exp(−t^2/(2σ^2)) with σ^2 = ||E[X^2]||, so deviations scale like σ and a dimension factor D appears. Method combines the Laplace-transform/Chernoff device with the cumulant-generating trick and a deep operator result (Lieb's theorem) to move expectations through a trace exponential. Rectangular cases reduce via the Hermitian dilation and intrinsic-dimension refinements.

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" chapters (9)

1. 0:00Introduction
2. 5:40Rademacher Series
3. 11:20Laplace Transform
4. 17:57Optimization
5. 28:42Concave function
6. 35:11CGF
7. 40:25Eigen Values
8. 44:46Examples
9. 48:34Technical Points

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