On Pfaffian random point fields
Probability
2014-07-17 v2
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.
Cite
@article{arxiv.1210.6603,
title = {On Pfaffian random point fields},
author = {Vladislav Kargin},
journal= {arXiv preprint arXiv:1210.6603},
year = {2014}
}
Comments
25 pages