For centered sub-Gaussian variables, the optimal ratio constants are sqrt(3/8) and sqrt(log 2), attained by the Gaussian and Rademacher laws respectively.
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Sharp constants relating the sub-Gaussian norm and the sub-Gaussian parameter
For centered sub-Gaussian variables, the optimal ratio constants are sqrt(3/8) and sqrt(log 2), attained by the Gaussian and Rademacher laws respectively.