# Sharp finite-sample concentration of independent variables

arXiv: https://arxiv.org/abs/2008.13293 · HTML: https://mlsanity.com/paper/2008.13293/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Aug 2020.

## Built on by (most cited first, 4 of 4)

- [E-Valuating Classifier Two-Sample Tests](https://mlsanity.com/paper/2210.13027/) (2022)
- [Information from coincidences](https://mlsanity.com/paper/2606.25042/) (2026)
- [Entropy, concentration, and learning: a statistical mechanics primer](https://mlsanity.com/paper/2409.18630/) (2024)
- [Laws of thermodynamics for exponential families](https://mlsanity.com/paper/2501.02071/) (2025)

## Abstract (arXiv)

We show an extension of Sanov's theorem on large deviations, controlling the tail probabilities of i.i.d. random variables with matching concentration and anti-concentration bounds. This result has a general scope, applies to samples of any size, and has a short information-theoretic proof using elementary techniques.