### 1. Introduction

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.

### 2. Gaussian Unitary/Orthogonal Ensembles (GUE) of random matrices

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.

### 3. Determinantal point processes

Point processes and their determinantal subclass. A class of
measures with determinantal structure. Correlation functions and
factorial moments. Gap probability: a Fredholm determinant.

### 4. Tracy-Widom distributions

Definition and properties. GUE Tracy-Widom distribution and
PainlevĂ© II equation.

### 5. Extension of determinantal processes

LinstrĂ¶m-Gessel-Viennot theorem. Dyson's Brownian Motion. Extended
determinantal point processes. An universal limit: the Airy2
process.

### 6. Applications to other processes

Polynuclear growth model. Totally asymmetric simple exclusion process.