Random walks are very popular models in many sciences. Think, for example, about a molecule of some gas traveling 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.
Fortunately or unfortunately, 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 mathematicians/statisticians.
Study of random walks with reinforcement, percolation theory
and random walks in random fields of traps - these are topics I am currently interested in. Of course, each of these topics is very broad, so if I were asked to specify what in particular I do, I would answer the following. The interesting problems which are easy to formulate, but not that easy to solve, those which require (sometimes) creation of new methods, more "to think" rather than "to calculate" problems. (If you participated in mathematical Olympiads, you know what I mean. If you did not, it is also not a problem.)
To get an idea about my past and on-going research, you can also visit the web page with my papers and preprints.
