Analysis and Probability Seminar

Abstract: Fractal percolation is a simple model giving stochastically self-similar sets. Starting with the unit cube in R^d, we subdivide the cube into n^d subcubes of side length 1/n. With probability p > 0 a subcube is kept (or discarded with probability 1 - p). The remaining subcubes are then again divided into n^d subcubes of side length 1/n^2. This process is continued ad infinitum and (under suitable assumptions) the remaining set is a compact non-empty subset of R^d. Many questions can be asked about this object, such as the existence and size of connected components, and I will survey some recent results on this model and its generalisations. Time permitting, I will also explain some brand new results with Istvan Kolossvary.