Equivalent symmetric kernels of determinantal point processes
Classical Analysis and ODEs
2019-06-27 v2 Mathematical Physics
math.MP
Abstract
Determinantal point processes are point processes whose correlation functions are given by determinants of matrices. The entries of these matrices are given by one fixed function of two variables, which is called the kernel of the point process. It is well-known that there are different kernels that induce the same correlation functions. We classify all the possible transformations of a kernel that leave the induced correlation functions invariant, restricting to the case of symmetric kernels.
Cite
@article{arxiv.1905.08162,
title = {Equivalent symmetric kernels of determinantal point processes},
author = {Marco Stevens},
journal= {arXiv preprint arXiv:1905.08162},
year = {2019}
}
Comments
8 pages. Small revision; the case of fields of characteristic 2 needed special attention and the general conjecture is now stated explicitly