From micro to macro: occurrence of universal physical laws. What does it mean that a physical system is well modeled by a random matrix ensemble? A few examples.
Definition. Distribution of eigenvalues. Macroscopic behavior: Wigner semi-circle law. Correlation functions: determinantal structure for GUE. Two important universal limits: bulk and edge scaling limits.
Point processes and their determinantal subclass. A class of measures with determinantal structure. Correlation functions and factorial moments. Gap probability: a Fredholm determinant.
Definition and properties. GUE Tracy-Widom distribution and Painlevé II equation.
Linström-Gessel-Viennot theorem. Dyson's Brownian Motion. Extended determinantal point processes. An universal limit: the Airy2 process.
Polynuclear growth model. Totally asymmetric simple exclusion process.