Hamilton-Jacobi scaling limits of Pareto peeling in 2D

2021/10/12 by Ahmed Bou‐Rabee, Bou-Rabee, Ahmed, Peter S. Morfe +1
Mathematics · Computer Science · #Point processes and geometric inequalities #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2110.06016

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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