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Universal concentration for sums under arbitrary dependence

Probability 2026-03-05 v2 Statistics Theory Statistics Theory

Abstract

We present a universal concentration bound for sums of random variables under arbitrary dependence, and we prove that it is asymptotically optimal for broad families of marginals admitting a uniform integrable tail-quantile envelope. The bound follows directly from the subadditivity of expected shortfall, a property well known in the risk-measure literature. Our sharpness result relies on an explicit construction of asymptotically extremal couplings. We furthermore provide practical sufficient conditions -- based on convex transformation order comparisons with exponential and power-law envelopes -- under which the bound admits simple, explicit tail profiles.

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Cite

@article{arxiv.2601.03518,
  title  = {Universal concentration for sums under arbitrary dependence},
  author = {Cosme Louart and Sicheng Tan},
  journal= {arXiv preprint arXiv:2601.03518},
  year   = {2026}
}

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R2 v1 2026-07-01T08:53:36.490Z