Sharp constants relating the sub-Gaussian norm and the sub-Gaussian parameter
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911045449154560 |
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| author | Leskelä, Lasse Zhukov, Matvei |
| author_facet | Leskelä, Lasse Zhukov, Matvei |
| contents | We determine the optimal constants in the classical inequalities relating the sub-Gaussian norm \(\|X\|_{ψ_2}\) and the sub-Gaussian parameter \(σ_X\) for centered real-valued random variables. We show that \(\sqrt{3/8} \cdot \|X\|_{ψ_2} \le σ_X \le \sqrt{\log 2} \cdot \|X\|_{ψ_2}\), and that both bounds are sharp, attained by the standard Gaussian and Rademacher distributions, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05928 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp constants relating the sub-Gaussian norm and the sub-Gaussian parameter Leskelä, Lasse Zhukov, Matvei Probability Statistics Theory 60E05, 60E15 We determine the optimal constants in the classical inequalities relating the sub-Gaussian norm \(\|X\|_{ψ_2}\) and the sub-Gaussian parameter \(σ_X\) for centered real-valued random variables. We show that \(\sqrt{3/8} \cdot \|X\|_{ψ_2} \le σ_X \le \sqrt{\log 2} \cdot \|X\|_{ψ_2}\), and that both bounds are sharp, attained by the standard Gaussian and Rademacher distributions, respectively. |
| title | Sharp constants relating the sub-Gaussian norm and the sub-Gaussian parameter |
| topic | Probability Statistics Theory 60E05, 60E15 |
| url | https://arxiv.org/abs/2507.05928 |