Sharp small-deviation inequalities for sums of independent nonnegative random variables
- Published
- Source
- arXiv
- Paper number
- 737
- Field
- Research
- arXiv ID
- 2607.23980
Key points
- It combined the exact Dirichlet calibration theorem of Vlassis and Thomas with results from convex geometry, including Grünbaum's centroid theorem.
- Treating 0<δ<1 and δ≥1 separately, it proved explicit lower bounds on small-deviation probabilities for sums of independent nonnegative random variables.
- For δ≥1, the lower bound is optimal for every n and is at least 1/e, settling Feige's conjecture.
- The result provides a sharp reference for analyzing the lower tails of sums of independent nonnegative random variables.
- However, optimality for every n is established only for δ≥1, and the lower bound in the range 0<δ<1 has not been proved equally sharp.
Paper links
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