# Sharp Concentration Results for Heavy-Tailed Distributions

arXiv: https://arxiv.org/abs/2003.13819 · HTML: https://mlsanity.com/paper/2003.13819/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2020.

## Built on by (most cited first, 15 of 15)

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- [Sublinear Algorithms for Wasserstein and Total Variation Distances: Applications to Fairness and Privacy Auditing](https://mlsanity.com/paper/2503.07775/) (2025)
- [Stochastic Weakly Convex Optimization Under Heavy-Tailed Noises](https://mlsanity.com/paper/2507.13283/) (2025)
- [Tail-Aware Information-Theoretic Bounds for LLM Alignment under Heavy-Tailed Rewards](https://mlsanity.com/paper/2604.10727/) (2026)

## Abstract (arXiv)

We obtain concentration and large deviation for the sums of independent and identically distributed random variables with heavy-tailed distributions. Our concentration results are concerned with random variables whose distributions satisfy mathbbP(X>t) ≤ rm e- I(t), where I: ℝ rightarrow ℝ is an increasing function and I(t)/t rightarrow α ∈ [0, ∞) as t rightarrow ∞. Our main theorem can not only recover some of the existing results, such as the concentration of the sum of subWeibull random variables, but it can also produce new results for the sum of random variables with heavier tails. We show that the concentration inequalities we obtain are sharp enough to offer large deviation results for the sums of independent random variables as well. Our analyses which are based on standard truncation arguments simplify, unify and generalize the existing results on the concentration and large deviation of heavy-tailed random variables.