TV homogenization inequalities
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917293119766528 |
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| author | Kontorovich, Aryeh |
| author_facet | Kontorovich, Aryeh |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04079 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | TV homogenization inequalities Kontorovich, Aryeh Probability 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. |
| title | TV homogenization inequalities |
| topic | Probability |
| url | https://arxiv.org/abs/2601.04079 |