AI helps mathematicians find simpler proof for first-passage percolation variance problem open since 1993
Hesamation · x · 2026-11-02
Mathematicians Scott Armstrong and Ahmed Bou-Rabee were formalizing the 200-page Basu-Sidoravicius-Sly (2023) proof of first-passage percolation variance bounds in Lean when AI agents (Astra) helped discover an entirely different, simpler approach.
- The new proof (arXiv:2610.42124) shows that in rotationally invariant first-passage percolation on R^d with d≥2, passage time variance scales sublinearly, at most n^(1-ε) — extending the prior 2D result to all dimensions for a class of models
- The problem dates back to Kesten's 1993 mention and had resisted proof for decades
- The argument combines the Benjamini-Kalai-Schramm averaging technique with Benaim-Rossignol's logarithmic improvement of the Efron-Stein inequality, replacing the original geodesic chaos argument
- The general problem remains open
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