On Hydrodynamic Limits of Young Diagrams
Abstract
We consider a family of stochastic models of evolving twodimensional 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 by several over the years. The purpose of this article is to study corresponding `dynamical' limits of which less is understood. We show that the hydrodynamic scaling limits of the diagram shape functions may be described by different types parabolic PDEs, depending on the energy structure.
 Publication:

arXiv eprints
 Pub Date:
 September 2018
 arXiv:
 arXiv:1809.03592
 Bibcode:
 2018arXiv180903592F
 Keywords:

 Mathematical Physics;
 Mathematics  Probability;
 60K35;
 82C22
 EPrint:
 43 pages, 4 figures