Equivalence of Ensembles Under Inhomogeneous Conditioning and Its Applications to Random Young Diagrams

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1 Citation (Scopus)

Abstract

We prove the equivalence of ensembles or a realization of the local equilibrium for Bernoulli measures on ℤ conditioned on two conserved quantities under the situation that one of them is spatially inhomogeneous. For the proof, we extend the classical local limit theorem for a sum of Bernoulli independent sequences to those multiplied by linearly growing weights. The motivation comes from the study of random Young diagrams and their evolutional models, which were originally suggested by Herbert Spohn. We discuss the relation between our result and the so-called Vershik curve which appears in a scaling limit for height functions of two-dimensional Young diagrams. We also discuss a related random dynamics.

Original languageEnglish
Pages (from-to)588-609
Number of pages22
JournalJournal of Statistical Physics
Volume154
Issue number1-2
DOIs
Publication statusPublished - 2014
Externally publishedYes

Fingerprint

Young Diagram
conditioning
Bernoulli
Conditioning
equivalence
Ensemble
diagrams
Equivalence
Local Limit Theorem
Local Equilibrium
Conserved Quantity
Scaling Limit
theorems
Linearly
scaling
Curve
curves
Model

Keywords

  • Equivalence of ensembles
  • Local equilibrium
  • Local limit theorem
  • Vershik curve
  • Young diagram

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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AB - We prove the equivalence of ensembles or a realization of the local equilibrium for Bernoulli measures on ℤ conditioned on two conserved quantities under the situation that one of them is spatially inhomogeneous. For the proof, we extend the classical local limit theorem for a sum of Bernoulli independent sequences to those multiplied by linearly growing weights. The motivation comes from the study of random Young diagrams and their evolutional models, which were originally suggested by Herbert Spohn. We discuss the relation between our result and the so-called Vershik curve which appears in a scaling limit for height functions of two-dimensional Young diagrams. We also discuss a related random dynamics.

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