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

• Tomoyuki Shirai ^[1] ; Yoichiro Takahashi ^[2]
  1. [1] Tokyo Institute of Technology

     Tokyo Institute of Technology

     Japón

     
  2. [2] Kyoto University

     Kyoto University

     Kamigyō-ku, Japón

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 31, Nº. 3, 2003, págs. 1533-1564
• Idioma: inglés
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• Resumen

  • 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.