Minimizers of Convex Functionals Arising in Random Surfaces

TL;DR

This paper studies the regularity of minimizers for specific non-smooth convex functionals in two dimensions, with applications to surface tensions in models of random surfaces and tilings.

Contribution

It provides new regularity results for minimizers of convex functionals relevant to random surface models, extending understanding in this area.

Findings

Establishes regularity properties of minimizers in two-dimensional convex functionals.

Applies results to surface tensions in random surface and tiling models.

Enhances theoretical understanding of convex functional minimization in stochastic geometry.

Abstract

We investigate regularity of minimizers in two dimensions for certain classes of non-smooth convex functionals. In particular our results apply to the surface tensions that appear in recent works on random surfaces and random tilings of Kenyon, Okounkov and others