Concentration Inequalities for Ultra Log-Concave Distributions

2021/04/11 by Aravinda, Heshan, Marsiglietti, Arnaud, Melbourne, James · 3 citations
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2104.05054

Abstract

We establish concentration inequalities in the class of ultra log-concave distributions. In particular, we show that ultra log-concave distributions satisfy Poisson concentration bounds. As an application, we derive concentration bounds for the intrinsic volumes of a convex body, which generalizes and improves a result of Lotz, McCoy, Nourdin, Peccati, and Tropp (2019).

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