Concentration Inequalities for Ultra Log-Concave Distributions

Heshan Aravinda, Arnaud Marsiglietti, James Melbourne

Published 2021-04-11Version 1

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).