Lasse Leskelä

Sharp constants relating the sub-Gaussian norm and the sub-Gaussian parameter

• L Leskelä, M Zhukov
• arXiv:2507.05928

Abstract

We determine the optimal constants in the classical inequalities relating the sub-Gaussian norm ‖X‖_ψ₂ and the sub-Gaussian parameter σ_X for centered real-valued random variables. We show that (3/8)^1/2 · ‖X‖_ψ₂ ≤ σ_X ≤ (log 2)^1/2 · ‖X‖_ψ₂, and that both bounds are sharp, attained by the standard Gaussian and Rademacher distributions, respectively.