Breadcrumb
Random walks in random media
Supervisor: Stanislav Volkov
Theme: Applied Probability
Random walks are very popular models in many sciences. Think, for example, about a molecule of some gas travelling and colliding with and reflecting from other molecules. Or observe a drunkard who tries to find his way home, choosing his direction randomly at each intersection: will he eventually hit his door or not? Typically, it is assumed that the media in which the walker goes (the gas in the first case and the streets of the town in the second) is given and is not random.
Unfortunately for new researchers, most of problems of that kind are solved by now. That is why nowadays scientists turned to more sophisticated models, where the media itself, or the rules of the walk are random. On one hand, this allows us to study more sophisticated phenomena observed in the world. On the other hand, this approach brings about really interesting problems, many of them are still open and constitute a challenge for a probabilist.