On Pfaffian random point fields

Abstract

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.

25 pages

References in corpus (2)

• Determinantal Processes and Independence
• Eynard-Mehta theorem, Schur process, and their pfaffian analogs

Cited by in corpus (5)

• The lower tail of the half-space KPZ equation
• Local Central Limit Theorem for Determinantal Point Processes
• Pfaffian Point Processes from Free Fermion Algebras: Perfectness and Conditional Measures
• On sampling determinantal and Pfaffian point processes on a quantum computer
• A 3D Ginibre point field