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Bibliographic Details
Main Authors: Deshayes, Aurelia, Frevenza, Nicolás, Miranda, Alfredo, Rossi, Julio D.
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2602.07696
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Table of Contents:
  • In this paper we approximate the convex envelope of a boundary datum inside a bounded domain in the Euclidean space. We work with a random graph that is obtained as random points with uniform distribution that are connected by proximity ($x\sim y$ when $|x-y|<r$). On the graph we solve an equation (that approximate the first eigenvalue of the Hessian of a smooth function) with an exterior datum. Under appropriate assumptions on $r$ we show that the unique solution to the equation in the graph converges to the convex envelope of the boundary datum as the number of points goes to infinity.