[2607.24528] On Feige's conjecture

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arXiv:2607.24528 (math)

[Submitted on 27 Jul 2026]

Title:On Feige's conjecture

Authors:Zipei Nie, Jiaye Wei<br>View a PDF of the paper titled On Feige's conjecture, by Zipei Nie and 1 other authors

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Abstract:We present a short proof of Feige's conjecture: for $n$ independent nonnegative random variables with expectation one, the probability that their sum is less than $n+1$ is at least $\left(\frac{n}{n+1}\right)^n\ge \frac{1}{e}$. The proof was obtained with the assistance of GPT-5.6 Sol and builds on the recent breakthrough of Vlassis and Thomas establishing Gaffke's conjecture on the finite-sample validity of a distribution-free $p$-value. We also discuss the implications of the subsequent work of Ming, Ramdas, Shen, Wang, and Waudby-Smith.

Comments:<br>8 pages, 0 figures

Subjects:

Probability (math.PR)

Cite as:<br>arXiv:2607.24528 [math.PR]

(or<br>arXiv:2607.24528v1 [math.PR] for this version)

https://doi.org/10.48550/arXiv.2607.24528

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arXiv-issued DOI via DataCite

Submission history<br>From: Zipei Nie [view email]<br>[v1]<br>Mon, 27 Jul 2026 15:07:59 UTC (7 KB)

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