Séminaire du 10 mars 03, Anatoly Vershik, St. Petersburg Department of Steklov Institute of Mathematics of Russian Academy of Sciences.

Fluctation of random partitions and related topics

There exist many results about random partitions and their limit shape for many natural statistics. The question of quantifying fluctuations around the mean is more delicate but for a class of so-called multiplicative statistics it has been solved recently. The link between random Young diagrams and random matrices allows us to connect this topic with a special type of random matrices which came from the theory random graphs and metric spaces. In the talk there will be explained the notion of universal objects (graphs, metric spaces) and its connection with random ones.