Title: On Hydrodynamic Limits of Young Diagrams
Abstract: We consider a family of stochastic models of evolving two-dimensional Young diagrams, given in terms of certain energies, with Gibbs invariant measures. `Static' scaling limits of the shape functions, under these Gibbs measures, have been much studied over the years. In this talk, we discuss corresponding `dynamical' limits which are less understood. We show that the hydrodynamic scaling limits of the Young diagram shape functions may be described by different types parabolic PDEs, depending on the energy structure.