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pengzhang91/Feige

Guanyang Wang, Peng Zhang

Palomar Registrypalomar/PALOMAR-2026-08-30-000002Aug 30, 2026math.PRscore 0

A Lean 4 formalization of the sharp unit-slack (delta = 1) small-deviation inequality for sums of independent nonnegative random variables. For every positive integer n and every independent family X_1, ..., X_n of measurable, integrable, nonnegative random variables satisfying E[X_i] = (n / (n + 1))^n and proves that this constant is optimal for each fixed n. This optimal dimension-dependent bound strengthens and implies Feige's 1/e conjecture. The repository also formalizes the Vlassis-Thomas exact calibration theorem and Grünbaum's centroid-halfspace inequality used in the proof.

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