Random point fields associated with certain Fredholm determinants II: Fermion shifts and their ergodic and Gibbs properties
Shirai, Tomoyuki ; Takahashi, Yoichiro
Ann. Probab., Tome 31 (2003) no. 1, p. 1533-1564 / Harvested from Project Euclid
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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.
Publié le : 2003-07-14
Classification:  Fredholm determinant,  Fermion process,  shift dynamical system,  Szegö's theorem,  metric entropy,  Gibbs property,  ergodic property.,  60G60,  60G55,  28D20,  82B05 
@article{1055425789,
     author = {Shirai, Tomoyuki and Takahashi, Yoichiro},
     title = {Random point fields associated with certain Fredholm determinants II: Fermion shifts and their ergodic and Gibbs properties},
     journal = {Ann. Probab.},
     volume = {31},
     number = {1},
     year = {2003},
     pages = { 1533-1564},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1055425789}
}

Shirai, Tomoyuki; Takahashi, Yoichiro. Random point fields associated with certain Fredholm determinants II: Fermion shifts and their ergodic and Gibbs properties. Ann. Probab., Tome 31 (2003) no. 1, pp.  1533-1564. http://gdmltest.u-ga.fr/item/1055425789/