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

研究成果: Contribution to journal › Article › 査読

9 被引用数 (Scopus)

抄録

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.

本文言語	英語
ページ（範囲）	725-770
ページ数	46
ジャーナル	Probability Theory and Related Fields
巻	165
号	3-4
DOI	https://doi.org/10.1007/s00440-015-0644-6
出版ステータス	出版済み - 8 1 2016

All Science Journal Classification (ASJC) codes

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

文献へのアクセス

10.1007/s00440-015-0644-6

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引用スタイル

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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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