A 3D Ginibre point field
Probability
2018-05-23 v1
Abstract
We introduce a three-dimensional random point field using the concept of the quaternion determinant. Orthogonal polynomials on the space of pure quaternions are defined, and used to construct a kernel function similar to the Ginibre kernel. We find explicit formulas for the polynomials and the kernel, and calculate their asymptotics in the bulk and at the center of coordinates.
Cite
@article{arxiv.1705.03118,
title = {A 3D Ginibre point field},
author = {Vladislav Kargin},
journal= {arXiv preprint arXiv:1705.03118},
year = {2018}
}
Comments
33 pages, 3 figures