Hamilton-Jacobi scaling limits of Pareto peeling in 2D

• 成果类型: Article
• 署名作者: Bou-Rabee, Ahmed; Morfe, Peter S.
• 署名单位: University of Chicago
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-023-01234-4
• 发表日期: 2024
• 页码: 235-307
• 关键词: equation continuum-limit; efficient points; weber problem; CONVERGENCE; block; rates

摘要

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 (Nonlinear Anal 141:88-108, 2016).