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.
"Random point fields associated with certain Fredholm determinants II: Fermion shifts and their ergodic and Gibbs properties." Ann. Probab. 31 (3) 1533 - 1564, July 2003. https://doi.org/10.1214/aop/1055425789