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

Tomoyuki Shirai, Yuichiro Takahashi

• 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.