Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals

TL;DR

This paper presents exact solutions for various models in statistical physics, including crystal growth, KPZ processes, and random matrices, using determinantal processes, providing insights into their universal behaviors.

Contribution

It introduces a unified method to analyze these models exactly, connecting different physical phenomena through determinantal processes.

Findings

Exact formulas for crystal facet edge statistics

Universal fluctuation results for KPZ growth

Connections established between random matrices and growth models

Abstract

Three models from statistical physics can be analyzed by employing space-time determinantal processes: (1) crystal facets, in particular the statistical properties of the facet edge, and equivalently tilings of the plane, (2) one-dimensional growth processes in the Kardar-Parisi-Zhang universality class and directed last passage percolation, (3) random matrices, multi-matrix models, and Dyson's Brownian motion. We explain the method and survey results of physical interest.