TY - JOUR
T1 - Absolute continuity and singularity of Palm measures of the Ginibre point process
AU - Osada, Hirofumi
AU - Shirai, Tomoyuki
PY - 2016/8/1
Y1 - 2016/8/1
N2 - 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.
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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U2 - 10.1007/s00440-015-0644-6
DO - 10.1007/s00440-015-0644-6
M3 - Article
AN - SCOPUS:84936864633
VL - 165
SP - 725
EP - 770
JO - Probability Theory and Related Fields
JF - Probability Theory and Related Fields
SN - 0178-8051
IS - 3-4
ER -