TY - JOUR
T1 - Absolute continuity and singularity of Palm measures of the Ginibre point process
AU - Osada, Hirofumi
AU - Shirai, Tomoyuki
N1 - Funding Information:
The authors would like to thank the anonymous referee for the careful reading and helpful comments which improve our manuscript. The first author (HO)’s work was supported in part by JSPS Grant-in-Aid for Scientific Research (A) No. 24244010 and (B) No. 21340031. The second author (TS)’s work was supported in part by JSPS Grant-in-Aid for Scientific Research (B) No. 22340020 and (B) No. 26287019.
Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.
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
SN - 0178-8051
VL - 165
SP - 725
EP - 770
JO - Probability Theory and Related Fields
JF - Probability Theory and Related Fields
IS - 3-4
ER -