Rangel Baldasso (PUC-Rio)
Percolation on Hierarchical Lattices

Percolation is a classical probabilistic model that describes the flow of a fuild through a porous medium. In general, the unders- tanding of this model strongly depends on the underlying discrete geometry. In this talk we examine families of hierarchical lattices, with focus on their percolative properties. The self-similar structure of these graphs leads naturally to recursive des- criptions of the model, which can be analyzed using ideas from dynamical systems. In particular, we exploit connections with hyperbolic dynamics to study critical phenomena and scaling properties of percolation. These tools are further combined with probabilistic methods to yield sharp results. No background in percolation is assumed, only basic knowledge of probability theory is required.