On Pfaffian Random Point Fields

V. Kargin

doi:10.1007/s10955-013-0900-z

On Pfaffian Random Point Fields

V. Kargin

Mathematics and Statistics

Binghamton University

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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.

Original language	English
Pages (from-to)	681-704
Number of pages	24
Journal	Journal of Statistical Physics
Volume	154
Issue number	3
DOIs	https://doi.org/10.1007/s10955-013-0900-z
State	Published - Feb 2014

Keywords

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

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10.1007/s10955-013-0900-z

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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.",

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AB - 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.

KW - Cauchy-Binet identity

KW - Determinantal field

KW - Determinantal identity

KW - Determinantal point process

KW - Gaussian symplectic ensemble

KW - Pfaffian point field

KW - Quaternion determinant

KW - Random matrices

KW - Random point field

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DO - 10.1007/s10955-013-0900-z

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VL - 154

SP - 681

EP - 704

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 3

ER -

On Pfaffian Random Point Fields

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Keywords

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