The negative association property for the absolute values of random variables equidistributed on a generalized Orlicz ball

TL;DR

This paper proves the negative association property for absolute values of random variables uniformly distributed on generalized Orlicz balls, leading to concentration inequalities and moment comparisons.

Contribution

It establishes the negative association property for generalized Orlicz balls, extending the theory and providing simpler proofs for related results.

Findings

Negative association property proven for generalized Orlicz balls

Derived strong concentration inequalities

Developed moment comparison inequalities

Abstract

Random variables equidistributed on convex bodies have received quite a lot of attention in the last few years. In this paper we prove the negative association property (which generalizes the subindependence of coordinate slabs) for generalized Orlicz balls. This allows us to give a strong concentration property, along with a few moment comparison inequalities. Also, the theory of negatively associated variables is being developed in its own right, which allows us to hope more results will be available. Moreover, a simpler proof of a more general result for $\ell_p^n$ balls is given.