Abstract
The first lecture began by introducing some of the simplest models, such as Eden's model or the ballistic deposition model, which describe the growth from a stable to an unstable medium. These models, which are very easy to simulate on a computer, enable us to observe the evolution of fluctuations at the boundary separating the stable from the unstable medium. The distribution of these fluctuations obeys scaling laws that are independent of the precise model considered, such as the Tracy Widom distribution discovered in the 1990s in a completely different context, that of random matrix theory. Theoretical and numerical approaches by Michael Prähofer and Herbert Spohn made it possible to predict the universal statistical laws of these fluctuations in dimension 1 + 1, and these laws were recently observed in experiments on liquid crystals by Kazumasa A. Takeushi and Masaki Sano. This first lecture went on to show how to relate the exponents governing these universal laws and to introduce the KPZ equation. It ended by explaining how the directional dependence of the growth rate predicts the macroscopic shape of growth domains.
