Ascending subsequences of permutations and Young tableaux

Asymptotic properties of the limit measures which appear in additive problems in partition theory and number theory can be considered in a geometric manner. There are different types of asymptotic behaviour: 'ergodic', including problems like the LLN and CLT, and 'non-ergodic', in which one can calculate the limit distribution and the boundary. All these kinds of examples appear in the context of random permutations and statistics on the partitions of integers or reals. -It turns out that completely different problems can give us the same limit measures.