Title: Universality in models of random growth
Abstract: Perhaps the greatest achievement of classical probability is the central limit theorem: under very mild assumptions, all properly normalized sums of independent and identically distributed random variables converge to the normal distribution. In the present time, a major focus of modern probability is to understand universal behavior of spatial stochastic models. In the last 30 years, it has been shown that special classes of random matrices, queuing systems, spatial growth models, and stochastic PDEs exhibit universal limiting statistics described by what is now called the Tracy-Widom distribution. In the last six years, richer objects whose one-point marginal distributions are given by the Tracy-Widom distribution have been constructed and shown to be the full scaling limit of several specialized models. Numerical and physical evidence suggests that this convergence should hold on a much broader scale, but proving such outside of the specialized models remains as a major open problem. In this talk, I will give a gentle introduction to this topic and describe my work to give new perspectives on this problem through another universal object known as the stationary horizon. Time permitting, I will discuss how the stationary horizon answers interesting questions about the fractal geometry of random growth models. Based on joint work with Ofer Busani and Timo Seppäläinen