In the late 70s Sergei Kerov and Anatoly Vershik initiated the study of asymptotics of representations of large symmetric groups. In other words: the asymptotics of large Young diagrams.
In the last decade some new methods were presented, by Phillipe Biane and others. These methods use connections with random matrices, noncommutative probability and Markov chains.
The lecture will give examples of some of these methods. In particular, we will discuss the connection with a recent work of A. Frumkin and A. Goldberger.