Hamilton-Jacobi scaling limits of Pareto peeling in 2D

Ahmed Bou-Rabee; Peter S. Morfe

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arXiv · 2110.06016

Hamilton-Jacobi scaling limits of Pareto peeling in 2D

Ahmed Bou-Rabee·Peter S. Morfe

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Abstract

Pareto hull peeling is a discrete algorithm, generalizing convex hull peeling, for sorting points in Euclidean space. We prove that Pareto peeling of a random point set in two dimensions has a scaling limit described by a first-order Hamilton-Jacobi equation and give an explicit formula for the limiting Hamiltonian, which is both non-coercive and non-convex. This contrasts with convex peeling, which converges to curvature flow. The proof involves direct geometric manipulations in the same spirit as Calder (2016).

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Ahmed Bou-Rabee, Peter S. Morfe. 2021-10-12. Hamilton-Jacobi scaling limits of Pareto peeling in 2D. https://arxiv.org/abs/2110.06016

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