Abstract:
I will present joint work with Jonas Sjöstrand where we consider a family of birth processes and birth-and-death processes on Young diagrams of integer partitions of $n$. This family incorporates three famous models from very different fields: Rost's totally asymmetric particle model (in discrete time), Simon's urban growth model, and Moran's infinite alleles model. We study stationary distributions and limit shapes as $n$ tends to infinity.