On Hydrodynamic Limits of Young Diagrams

On Hydrodynamic Limits of Young Diagrams

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 by several over the years. The purpose of this art...

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Bibliographic Details
Main Authors: Fatkullin, Ibrahim, Sethuraman, Sunder, Xue, Jianfei
Format: Journal Article
Language:English
Published: 10-09-2018
Subjects:
Mathematics - Mathematical Physics
Mathematics - Probability
Physics - Mathematical Physics
Online Access:Get full text
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Summary: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 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.
DOI:10.48550/arxiv.1809.03592