Random Growth Models and KPZ Universality

Irregular growth is a ubiquitous phenomenon in nature, from the growth of tumors, crystals, and bacterial colonies to the propagation of forest fires and the spread of water through a porous medium. Mathematical models of random growth have been a driving force in probability theory over the last sixty years and a rich source of important ideas. The analysis of random growth models began in the early 1960s with the introduction of the Eden model by Eden and first-passage percolation by Hammersley and Welsh. The field witnessed several breakthroughs in the 1980s and 1990s, from the introduction of more random growth models, including the Kardar, Parisi, and Zhang (KPZ) equation and the KPZ universality class, to the ground-breaking works of Tracy and Widom and of Baik, Deift, and Johansson, and the seminal works of Newman and coauthors. These results caused a flurry of activity and more analytical and geometrical tools were developed.