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

Tadahisa Funaki, Makiko Sasada

Research output: Contribution to journalArticle

7 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 Jun 28
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Fingerprint Dive into the research topics of 'Hydrodynamic Limit for an Evolutional Model of Two-Dimensional Young Diagrams'. Together they form a unique fingerprint.

  • Cite this