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

Tomoyuki Shirai; Yoichiro Takahashi

doi:10.1214/aop/1055425789

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 journal › Article › peer-review

62 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 language	English
Pages (from-to)	1533-1564
Number of pages	32
Journal	Annals of Probability
Volume	31
Issue number	3
DOIs	https://doi.org/10.1214/aop/1055425789
Publication status	Published - Jul 2003
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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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.",

author = "Tomoyuki Shirai and Yoichiro Takahashi",

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

Abstract

All Science Journal Classification (ASJC) codes

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