Couplings for determinantal point processes and their reduced Palm distributions with a view to quantifying repulsiveness
Keyword(s):
AbstractFor a determinantal point process (DPP) X with a kernel K whose spectrum is strictly less than one, André 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 to discuss the degree of repulsiveness in DPPs in terms of $\xi_u$, including Ginibre point processes and other specific parametric models for DPPs.
2020 ◽
Vol 378
(2166)
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pp. 20190059
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2015 ◽
Vol 52
(4)
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pp. 1003-1012
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2015 ◽
Vol 52
(04)
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pp. 1003-1012
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2019 ◽
pp. 305-318
2014 ◽
Vol 70
(a1)
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pp. C523-C523
2014 ◽
Vol 46
(3)
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pp. 832-845
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2014 ◽
Vol 46
(03)
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pp. 832-845
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