Random walks on fractals

Random walks (RWs) and related stochastic techniques have become ubiquitous tools in many areas of physics recently. Fractals are no exception. Random walks on fractals have an added interest: random walk trails (e.g. sample paths of Brownian motion) are themselves fractal in general, and interesting kinds of behavior emerge when they occur on fractal structures, in the form of scaling laws. In the case of random Factals, one has a “random walk on a random walk”. This is an instance of a so-called “random” random walk, in the study of which considerable progress has recently been made.