Directed random growth models on the plane

TL;DR

This paper surveys probabilistic laws and principles for models of moving interfaces on the plane, focusing on asymmetric particle systems like exclusion and Hammersley processes, and their growth models.

Contribution

It provides a comprehensive overview of large number laws, fluctuations, and large deviations for key interface growth models on the plane.

Findings

Summary of laws of large numbers for these models

Discussion of fluctuation results and their implications

Overview of large deviation principles in the context of interface growth

Abstract

This is a brief survey of laws of large numbers, fluctuation results and large deviation principles for asymmetric interacting particle systems that represent moving interfaces on the plane. We discuss the exclusion process, the Hammersley process and the related last-passage growth models.