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arXiv · 2306.00209

Exponential inequalities in probability spaces revisited

Ali Barki·Sergey G. Bobkov·Esther Bou Dagher·Cyril Roberto
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Abstract

We revisit several results on exponential integrability in probability spaces and derive some new ones. In particular, we give a quantitative form of recent results by Cianchi-Musil and Pick in the framework of Moser-Trudinger-type inequalities, and recover Ivanisvili-Russell's inequality for the Gaussian measure. One key ingredient is the use of a dual argument, which is new in this context, that we also implement in the discrete setting of the Poisson measure on integers.

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Ali Barki, Sergey G. Bobkov, Esther Bou Dagher, Cyril Roberto. 2023-05-31. Exponential inequalities in probability spaces revisited. https://arxiv.org/abs/2306.00209

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