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arXiv · 1705.03118

A 3D Ginibre point field

Vladislav Kargin
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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.

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Vladislav Kargin. 2017-05-08. A 3D Ginibre point field. https://doi.org/10.1007/s10955-018-2043-8

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