Random point fields associated with certain Fredholm determinants II: Fermion shifts and their ergodic and Gibbs properties

Tomoyuki Shirai, Yoichiro Takahashi

Research output: Contribution to journalArticle

39 Citations (Scopus)

Abstract

We construct and study a family of probability measures on the configuration space over countable discrete space associated with nonnegative definite symmetric operators via determinants. Under a mild condition they turn out unique Gibbs measures. Also some ergodic properties, including the entropy positivity, are discussed in the lattice case.

Original languageEnglish
Pages (from-to)1533-1564
Number of pages32
JournalAnnals of Probability
Volume31
Issue number3
DOIs
Publication statusPublished - Jul 1 2003

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Fredholm Determinant
Symmetric Operator
Gibbs Measure
Configuration Space
Positivity
Probability Measure
Fermions
Countable
Determinant
Non-negative
Entropy
Family
Operator

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Random point fields associated with certain Fredholm determinants II : Fermion shifts and their ergodic and Gibbs properties. / Shirai, Tomoyuki; Takahashi, Yoichiro.

In: Annals of Probability, Vol. 31, No. 3, 01.07.2003, p. 1533-1564.

Research output: Contribution to journalArticle

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