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math.PR2025
Sub-Poisson distributions: Concentration inequalities, optimal variance proxies, and closure properties
Lasse Leskelä, Ian Välimaa
We introduce a nonasymptotic framework for sub-Poisson distributions with moment generating function dominated by that of a Poisson distribution. At its core is a new notion of opt…
math.PR2025
Sharp constants relating the sub-Gaussian norm and the sub-Gaussian parameter
Lasse Leskelä, Matvei Zhukov
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 rand…