3 years ago

Couplings for determinantal point processes and their reduced Palm distributions with a view to quantifying repulsiveness.

Eliza O'Reilly, Jesper Møller

For a determinantal point process $X$ with a kernel $K$ whose spectrum is strictly less than one, Andr{\'e} Goldman has established a coupling to its reduced Palm process $X^u$ at a point $u$ with $K(u,u)>0$ so that almost surely $X^u$ is obtained by removing a finite number of points from $X$. We sharpen this result, assuming weaker conditions and establishing that $X^u$ can be obtained by removing at most one point from $X$, where we specify the distribution of the difference $\xi_u:=X\setminus X^u$. This is used for discussing the degree of repulsiveness in DPPs in terms of $\xi_u$, including Ginibre point processes and other specific parametric models for DPPs.

Publisher URL: http://arxiv.org/abs/1806.07347

DOI: arXiv:1806.07347v3

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