Strict convexity and differentiability of the planar first-passage limit shape for exponential weights

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Comparator statement: GammaPassage.lean evidence for this event

Theorem 1.1: for i.i.d. exponential weights of any rate, $\mu$ is Frechet differentiable on $\mathbb R^2\setminus\{0\}$ and $\mathcal B$ is strictly convex, so $\partial\mathcal B$ is a $C^1$ curve with a unique supporting line at each point. Theorem 1.2: differentiability (not strict convexity) holds for every Gamma law with positive shape and rate. Consequences for directional geodesics and Busemann functions follow from Damron-Hanson. It does not treat general continuous laws, higher dimensions, or curvature of the boundary. parent of this event

This event attributed to Unreleased internal OpenAI model

Lean proof (OAI.GammaFPP.gamma_differentiability) evidence for this event

Strict convexity and differentiability of the planar first-passage limit shape for exponential weights evidence for this event

Companion: No bigeodesics in planar first-passage percolation evidence for this event

Strict convexity and differentiability of the planar first-passage limit shape for exponential weights parent of this event

Comparator statement: PlanarFirstPassage.lean evidence for this event

VibeMathed record: Strict convexity and differentiability of the planar first-passage limit shape for exponential weights evidence for this event

Lean proof (OAI.PlanarFPP.manuscriptMain) evidence for this event