The scale invariant dynamics

Abstract
After the remarkable discoveries in equilibrium critical phenomena and the development of the Renormalization Group (RG) a branch of Statistical Physics has evolved towards the study of fractal growth and self-organization. The main models in this area are Diffusion Limited Aggregation, the Sandpile model, Invasion Percolation and the Kardar-Parisi-Zhang dynamics of rough surfaces. For these models the usual theoretical methods of equilibrium critical phenomena cannot be applied and new theoretical concepts are necessary. In the past years we have developed a new theoretical framework for non-ergodic dynamics and self-organization. A novel and essential concept consists in the Scale Invariant Dynamics, which is the dynamics that corresponds to coarse grained variables. In this lecture we describe the development and the properties of this concept in relation to the usual RG ideas and methods. We also discuss briefly its specific applications for each of the above mentioned models.