Sharp constants relating the sub-Gaussian norm and the sub-Gaussian parameter
Abstract
We determine the optimal constants in the classical inequalities relating the sub-Gaussian norm ‖X‖ψ2 and the sub-Gaussian parameter σX for centered real-valued random variables. We show that 3∕8⋅‖X‖ψ2≤σX≤ log2⋅‖X‖ψ2, and that both bounds are sharp, attained by the standard Gaussian and Rademacher distributions, respectively.
Fields of Study & Subjects
Probability and Statistical Research
Point processes and geometric inequalities
Probability and Risk Models
Publication details
- Journal / source
- Electronic Communications in Probability
- Volume
- 31
- Issue
- none
- Pages
- 1–11
- Publication date
- 1 January 2026
- Language
- EN