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Concentration for empirical spectral distributions

I have just updated my former post on the concentration for empirical spectral distributions. Surprisingly, the concentration of empirical spectral distributions of random matrices around their mean holds under very weak assumptions (independent rows). No moments assumptions, no Poincaré or log-Sobolev inequalities, no Talagrand concentration inequalities for convex Lipschitz functions. The brave Azuma-Hoeffding-McDiarmid bounded differences inequalities  are enough!

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