What is...a Supercritial Percolation Cluster?

This page hosts information on Nguyen Tuan Anh's talk "What is … a Supercritical Percolation Cluster?" at the "What is …?" seminar. The talk will take place on Friday, May 08, 1:00pm at the BMS Seminar Room MA 212 at TU Berlin. This talk will help you better understand the talk by Nina Gantert, which will start at 2pm.

Abstract

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.

Finally, the talk requires no background in probability theory.

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