Hydrodynamic Limit for an Evolutional Model of Two-Dimensional Young Diagrams

Tadahisa Funaki, Makiko Sasada

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We construct dynamics of two-dimensional Young diagrams, which are naturally associated with their grandcanonical ensembles, by allowing the creation and annihilation of unit squares located at the boundary of the diagrams. The grandcanonical ensembles, which were introduced by Vershik [17], are uniform measures under conditioning on their size (or equivalently, area). We then show that, as the averaged size of the diagrams diverges, the corresponding height variable converges to a solution of a certain non-linear partial differential equation under a proper hydrodynamic scaling. Furthermore, the stationary solution of the limit equation is identified with the so-called Vershik curve. We discuss both uniform and restricted uniform statistics for the Young diagrams.

Original languageEnglish
Pages (from-to)335-363
Number of pages29
JournalCommunications in Mathematical Physics
Volume299
Issue number2
DOIs
Publication statusPublished - 2010
Externally publishedYes

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Young Diagram
Hydrodynamic Limit
diagrams
hydrodynamics
Ensemble
Diagram
Diverge
Stationary Solutions
Annihilation
Nonlinear Partial Differential Equations
Conditioning
Hydrodynamics
conditioning
Model
Scaling
partial differential equations
Statistics
Converge
Curve
Unit

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Hydrodynamic Limit for an Evolutional Model of Two-Dimensional Young Diagrams. / Funaki, Tadahisa; Sasada, Makiko.

In: Communications in Mathematical Physics, Vol. 299, No. 2, 2010, p. 335-363.

Research output: Contribution to journalArticle

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