Wioletta Ruszel: Abelian sandpile model on Galton-Watson trees

The concept of self-organized criticality was introduced by Bak, Tang and Wiesenfeld in 1987 as an explanation for the existence of a certain type of noise and power-law behaviour in power spectra in particular physical systems. It captures the idea that certain physical systems can drive themselves into a critical state which shares several properties of equilibrium systems at the critical point such as power-law decay of correlations. Models of self-organized criticality provide a mechanism which can be used to explain the emergence of complexity in many natural phenomena.

One of the most exciting applications of the sandpile dynamics is to model neuronal communication in the brain.

In this talk we will review some recent results and work in progress on power-law behaviour of avalanche size distributions random trees. This is joint work with Antal Jarai, Frank Redig and Ellen Saada.