User-Friendly Tools for Random Matrices III

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" summary

Proves a usable bound: for a Rademacher series X = sum εi Ai the paper builds an exchangeable pairs construction (replace one εi) to form a matrix-Stein pair with α = 1/n, computes the conditional variance ΔX = sum Ai^2 = E[X^2], and shows E[tr(X^{2p})]^{1/2p} ≤ √(2p−1) · E[tr(ΔX^p)]^{1/2p}. Constant is within √e of optimal, extends to rectangular matrices and some dependent settings, and yields spectral-norm tail control via moment-to-norm conversion.

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" chapters (7)

1. 0:00Introduction to Matrix Stein
2. 2:37Matrix Khintchine Inequality
3. 9:27Exchangeable Pairs
4. 16:03Stein Pair Method
5. 24:05Mean Value Trace Inequality
6. 28:09Matrix Burkholder Inequality
7. 35:44Conclusion and Discussion

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