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

Tadahisa Funaki, Makiko Sasada

研究成果: Article査読

8 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)335-363
ページ数29
ジャーナルCommunications in Mathematical Physics
299
2
DOI
出版ステータスPublished - 2010 6 28
外部発表はい

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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