Tuan Anh Nguyen (TU Berlin)

2015/05/08, 13:00, Before the BMS Friday Colloquium by Prof. Nina Gantert

TU Berlin, at the BMS seminar room (MA 212)

With a lot of pictures my talk will explain you what a supercritical percolation cluster is and give you an example of two random walks among random conductances on this cluster: i) the constant speed and ii) the variable speed random walk, which are typical examples of discrete and continuous time Markov chains. (They may not be exactly the objects in Nina Gantert's talk, but they will give you some feeling about this field.)

Very easy examples will show one of the main difficulties when studying the macroscopic properties of the random walks. That is, the trap problem, which can be roughly understood as follows. While the constant speed random walk stays a very long time in very high conductances, the variable speed one cannot easily get out of very low conductances. To get rid of this difficulty, one needs some assumptions on the law of the random conductances, which is introduced at the end of the talk.