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Total Variation Distance between Product Distributions: an Analytic Proxy
Abstract
We characterize, up to universal constants, the total variation distance between finite products of arbitrary probability measures by a simple formula. A theorem of Latala reduces this expression to one scalar equation. As an application, we characterize the sample complexity of equal-prior binary hypothesis testing uniformly in the weak-detection regime, where squared Hellinger distance alone does not determine the answer, and also characterize the TV distance between multinomial distributions.
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BibTeX
@misc{avital2026total,
title = {{Total Variation Distance between Product Distributions: an Analytic Proxy}},
author = {Ariel Avital and Aryeh Kontorovich and Roman Vershynin and Guangyi Zou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21049},
eprint = {2609.21049},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21049},
}
RIS
TY - UNPB
TI - Total Variation Distance between Product Distributions: an Analytic Proxy
AU - Ariel Avital
AU - Aryeh Kontorovich
AU - Roman Vershynin
AU - Guangyi Zou
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.21049
UR - https://arxiv.org/abs/2609.21049
AB - We characterize, up to universal constants, the total variation distance between finite products of arbitrary probability measures by a simple formula. A theorem of Latala reduces this expression to one scalar equation. As an application, we characterize the sample complexity of equal-prior binary hypothesis testing uniformly in the weak-detection regime, where squared Hellinger distance alone does not determine the answer, and also characterize the TV distance between multinomial distributions.
ER -