Abstract
The fourth lecture began by establishing the equivalence between the stochastic heat equation and the KPZ equation. Starting with the case of directed polymers, it was shown that the KPZ equation reduces, in the high-temperature limit, to a linear equation, the Edwards Wilkinson equation. This equation can obviously be solved in any dimension. Further development of the high-temperature equation shows that the corrections explode in the low-dimensional range. The rest of the lecture was devoted to other simplified versions of the KPZ equation: the Burgers equation with or without viscosity, which gives rise to shock waves, and to discussion of the various possible descriptions of these shock waves at the miscroscopic scale.
