The limit shape of convex hull peeling
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Abstract (arXiv)
We prove that the convex peeling of a random point set in dimension d approximates motion by the 1/(d + 1) power of Gaussian curvature. We use viscosity solution theory to interpret the limiting partial differential equation. We use the Martingale method to solve the cell problem associated to convex peeling. Our proof follows the program of Armstrong-Cardaliaguet for homogenization of geometric motions, but with completely different ingredients.
Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). First posted on arXiv 21 May 2018.
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Citing papers per year: 2021: 2; 2022: 2; 2023: 1; 2024: 1.
6 papers.
- 2022Hamilton-Jacobi equations on graphs with applications to semi-supervised learning and data depthcited by 7
- 2021Boundary Estimation from Point Clouds: Algorithms, Guarantees and Applicationscited by 4
- 2021Tukey Depths and Hamilton-Jacobi Differential Equationscited by 3
- 2024Numerical solution of a PDE arising from prediction with expert advicecited by 3
- 2022Eikonal depth: an optimal control approach to statistical depthscited by 1
- 2023RACH-Space: Reconstructing Adaptive Convex Hull Space with Applications in Weak Supervisioncited by 0
- 2024Numerical solution of a PDE arising from prediction with expert advice9 Jun 2024
- 2023RACH-Space: Reconstructing Adaptive Convex Hull Space with Applications in Weak Supervision10 Jul 2023
- 2022Hamilton-Jacobi equations on graphs with applications to semi-supervised learning and data depth17 Feb 2022
- 2022Eikonal depth: an optimal control approach to statistical depths14 Jan 2022
- 2021Boundary Estimation from Point Clouds: Algorithms, Guarantees and Applications5 Nov 2021
- 2021Tukey Depths and Hamilton-Jacobi Differential Equations4 Apr 2021