Asymptotics for random combinatorial structures

How does a random partition of a large integer look? I will present asymptotic results and variational problems for this question, obtained in a joint work with A. Vershik and O. Zeitouni. The techniques involve some combinatorics and mostly probability. I shall also survey some known results about asymptotics of this and other random combinatorial structures, such as permutations, forests of trees and convex polygons with integer vertices. If time permits I will outline possible extensions of this approach to some of the above mentioned structures and related open questions.