Random metric geometries on the plane and Kardar-Parisi-Zhang universality

TL;DR

This paper explores random metric geometries on the plane and their connection to Kardar-Parisi-Zhang universality, providing insights into geometric structures and stochastic growth phenomena.

Contribution

It introduces new perspectives on the geometric properties of models related to KPZ universality and discusses their implications in mathematical physics.

Findings

Identification of geometric structures linked to KPZ universality

New insights into random metric geometries on the plane

Connections established between geometry and stochastic growth models

Abstract

This is the article with the same title which is scheduled to appear in the January 2022 issue of the AMS Notices, with additional references which could not be provided in the accepted version due to space constraints. The figures in this article were made collaboratively with Milind Hegde.