Absolute continuity and singularity of Palm measures of the Ginibre point process

Hirofumi Osada; Tomoyuki Shirai

doi:10.1007/s00440-015-0644-6

Absolute continuity and singularity of Palm measures of the Ginibre point process

Hirofumi Osada, Tomoyuki Shirai

Research output: Contribution to journal › Article

9 Citations (Scopus)

Abstract

We prove a dichotomy between absolute continuity and singularity of the Ginibre point process G and its reduced Palm measures { G_x, x∈ C^ℓ, ℓ= 0 , 1 , 2 … } , namely, reduced Palm measures G_x and G_y for x∈ C^ℓ and y∈ Cⁿ are mutually absolutely continuous if and only if ℓ= n; they are singular each other if and only if ℓ≠ n. Furthermore, we give an explicit expression of the Radon–Nikodym density dG_x/ dG_y for x, y∈ C^ℓ.

Original language	English
Pages (from-to)	725-770
Number of pages	46
Journal	Probability Theory and Related Fields
Volume	165
Issue number	3-4
DOIs	https://doi.org/10.1007/s00440-015-0644-6
Publication status	Published - Aug 1 2016

All Science Journal Classification (ASJC) codes

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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Osada, H., & Shirai, T. (2016). Absolute continuity and singularity of Palm measures of the Ginibre point process. Probability Theory and Related Fields, 165(3-4), 725-770. https://doi.org/10.1007/s00440-015-0644-6

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AU - Shirai, Tomoyuki

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AB - We prove a dichotomy between absolute continuity and singularity of the Ginibre point process G and its reduced Palm measures { Gx, x∈ Cℓ, ℓ= 0 , 1 , 2 … } , namely, reduced Palm measures Gx and Gy for x∈ Cℓ and y∈ Cn are mutually absolutely continuous if and only if ℓ= n; they are singular each other if and only if ℓ≠ n. Furthermore, we give an explicit expression of the Radon–Nikodym density dGx/ dGy for x, y∈ Cℓ.

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