Concentration inequalities for ultra log-concave distributions
Volume 265 / 2022
Studia Mathematica 265 (2022), 111-120 MSC: Primary 60E15, 60F10; Secondary 52A40. DOI: 10.4064/sm210605-2-10 Published online: 31 January 2022
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).