TV homogenization inequalities
Probability
2026-02-26 v3
Abstract
We study the total variation distance under two information-erasing maps on inhomogeneous Bernoulli product measures: summation and homogenization. While summation is a Markov kernel and hence satisfies the usual data processing inequality, homogenization -- which maps each Bernoulli parameter to the cumulative mean -- is not. Nevertheless, we prove that the homogenization map also reduces the TV distance, up to a universal constant. The argument is based on an explicit two-sided control of the TV distance between Poisson binomials, obtained via a parameter interpolation and a second-moment extraction lemma.
Cite
@article{arxiv.2601.04079,
title = {TV homogenization inequalities},
author = {Aryeh Kontorovich},
journal= {arXiv preprint arXiv:2601.04079},
year = {2026}
}