Kadanoff Sand Pile Model : Avalanches and Fixed Points

Kadanoff Sand Pile Models (KSPM) is a set of discrete – in space and time – dynamical systems describing the evolution from a finite number N of stacked grains to a stable configuration. The goal is to find a closed formula describing asymptotically the fixed points according to N. The main interest of sand pile models relies on the difficulty of understanding the evolution, despite the simplicity of the local rules. In this talk we will try to figure out why a wavy shape emerges on fixed points.

Joint work with Eric Rémila.