Limit shape of partitions via bijections

We compute the limit shape for several classes of restricted integer partitions. There are many earlier results in this direction for different types of restrictions. Our approach is quite different and utilizes certain classes of bijections which map limit shapes continuously in the plane.
In this talk I will give an overview of previous results on the subject. I will then discuss the new results we obtained with Stephen DeSalvo. Notably, we compute limit shapes for partitions with given differences in part size. We also study limit shapes with different scaling functions.
The talk will be in Russian with slides in English. We will assume no prior knowledge of the subject.