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

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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

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

First available in Project Euclid: 12 June 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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