TV homogenization inequalities

Aryeh Kontorovich

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arXiv · 2601.04079

TV homogenization inequalities

Aryeh Kontorovich

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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.

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Aryeh Kontorovich. 2026-01-07. TV homogenization inequalities. https://arxiv.org/abs/2601.04079

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