On Pfaffian Random Point Fields

作者：Kargin V^*

来源：Journal of Statistical Physics, 2014, 154(3): 681-704.

DOI：10.1007/s10955-013-0900-z

• Determinantal field
• Determinantal point process
• Random point field
• Pfaffian point field
• Quaternion determinant
• Cauchy-Binet identity
• Determinantal identity
• Gaussian symplectic ensemble
• Random matrices

We study Pfaffian random point fields by using the Moore-Dyson quaternion determinants. First, we give sufficient conditions that ensure that a self-dual quaternion kernel defines a valid random point field, and then we prove a CLT for Pfaffian point fields. The proofs are based on a new quaternion extension of the Cauchy-Binet determinantal identity. In addition, we derive the Fredholm determinantal formulas for the Pfaffian point fields which use the quaternion determinant.

• 出版日期2014-2