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 shown in the literature. The purpose of this article is to study corresponding, but less understood, ‘dynamical’ limits. We show that the hydrodynamic scaling limits of the diagram shape functions may be described by different types of parabolic PDEs, depending on the energy structure.
"On hydrodynamic limits of Young diagrams." Electron. J. Probab. 25 1 - 44, 2020. https://doi.org/10.1214/20-EJP455