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2020 On hydrodynamic limits of Young diagrams
Ibrahim Fatkullin, Sunder Sethuraman, Jianfei Xue
Electron. J. Probab. 25: 1-44 (2020). DOI: 10.1214/20-EJP455

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 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.

Citation

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Ibrahim Fatkullin. Sunder Sethuraman. Jianfei Xue. "On hydrodynamic limits of Young diagrams." Electron. J. Probab. 25 1 - 44, 2020. https://doi.org/10.1214/20-EJP455

Information

Received: 11 May 2019; Accepted: 12 April 2020; Published: 2020
First available in Project Euclid: 5 May 2020

zbMATH: 1441.60078
MathSciNet: MR4095054
Digital Object Identifier: 10.1214/20-EJP455

Subjects:
Primary: 60K35, 82C22

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