On Feige's conjecture
- Published
- Source
- arXiv
- Paper number
- 738
- Field
- Research
- arXiv ID
- 2607.24528
Key points
- It constructed a short proof by connecting Vlassis and Thomas's distribution-free p-value result to the random-variable-sum problem in Feige's conjecture.
- It showed that the probability that the sum of n independent nonnegative random variables, each with expectation 1, is less than n+1 is at least (n/(n+1))^n.
- Because this lower bound is at least 1/e, it establishes Feige's conjecture, posed in 2004.
- It shows how resolving Gaffke's conjecture in statistics can lead to a proof of a probability inequality, and GPT-5.6 Sol assisted the proof search.
- However, the central theorem focuses on Feige's conjecture with threshold n+1, rather than resolving the full range of more general small-deviation parameters.
Paper links
External research summaries. These are not HDATF publications or measured product results.