Anatoly Vershik, IHES, Bures-sur-Yvette

Limit Shape Theorems for Partitions

Many combinatorial and geometrical problems can be reduced to a problem about partitions of natural numbers or vectors, etc. The main asymptotic question is the behaviour of the shape of such a partition when the statistics or dynamics are fixed. This leads us to the problems of limit shapes. Example: what is the typical limit shape of the uniformly distributed classical partiton of the natural numbers? An explicit answer can be given.