Abstract
The second lecture introduced two other families of models that fall within the universality class of the KPZ equation: asymmetric exclusion processes and directed polymers in random media. Exclusion models were proposed in the 1960s to describe the directed movement of enzymes along a DNA molecule. They have been extensively studied to understand the hydrodynamic boundary that bridges the gap between the microscopic and macroscopic worlds. What's more, they belong to a family of non-equilibrium models that we know exactly how to solve. By establishing a link between exclusion processes and growth models, we can determine exactly the set of exponents for the 1-dimensional growth problem + 1. Some striking results, such as Gunter M. Schütz's (1997) and Kurt Johansson's (2000) formula, were stated, providing a link to random matrix theory. The rest of the lecture was devoted to the question of directed polymers in a random environment, showing in particular the link with the problem of the statistical law of the largest increasing subsequence of a random permutation.
