Gibbsianness of fermion random point fields |
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Authors: | Hyun Jae Yoo |
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Institution: | (1) University College, Yonsei University, 134 Shinchon-dong, Seodaemoon-gu, Seoul, 120-749, Korea |
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Abstract: | We consider fermion (or determinantal) random point fields on Euclidean space ℝd. Given a bounded, translation invariant, and positive definite integral operator J on L2(ℝd), we introduce a determinantal interaction for a system of particles moving on ℝd as follows: the n points located at x1,· · ·,xn ∈ ℝd have the potential energy given by where j(x−y) is the integral kernel function of the operator J. We show that the Gibbsian specification for this interaction is well-defined. When J is of finite range in addition, and for d≥2 if the intensity is small enough, we show that the fermion random point field corresponding to the operator J(I+J)−1 is a Gibbs measure admitted to the specification. |
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Keywords: | 60K35 82B21 |
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