The Annals of Probability

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

Tomoyuki Shirai and Yoichiro Takahashi

Full-text: Open access

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.

Article information

Source
Ann. Probab. Volume 31, Number 3 (2003), 1533-1564.

Dates
First available in Project Euclid: 12 June 2003

Permanent link to this document
https://projecteuclid.org/euclid.aop/1055425789

Digital Object Identifier
doi:10.1214/aop/1055425789

Mathematical Reviews number (MathSciNet)
MR1989442

Zentralblatt MATH identifier
1051.60053

Subjects
Primary: 60G60: Random fields 60G55: Point processes
Secondary: 28D20: Entropy and other invariants 82B05: Classical equilibrium statistical mechanics (general)

Keywords
Fredholm determinant Fermion process shift dynamical system Szegö's theorem metric entropy Gibbs property ergodic property.

Citation

Shirai, Tomoyuki; Takahashi, Yoichiro. Random point fields associated with certain Fredholm determinants II: Fermion shifts and their ergodic and Gibbs properties. Ann. Probab. 31 (2003), no. 3, 1533--1564. doi:10.1214/aop/1055425789. https://projecteuclid.org/euclid.aop/1055425789.


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References

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  • KANAZAWA, ISHIKAWA 920-1192 JAPAN E-MAIL: shirai@kenroku.kanazawa-u.ac.jp RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES Ky OTO UNIVERSITY SAKy O-KU, Ky OTO 606-8502 JAPAN E-MAIL: takahasi@kurims.ky oto-u.ac.jp