Absolute continuity and singularity of Palm measures of the Ginibre point process
We prove a dichotomy between absolute continuity and singularity of the Ginibre point
process GG and its reduced Palm measures {G _ x, x ∈ C^ ℓ, ℓ= 0, 1, 2 ...\} G x, x∈ C ℓ, ℓ= 0,
1, 2…, namely, reduced Palm measures G _ x G x and G _ y G y for x ∈ C^ ℓ x∈ C ℓ and y
∈ C^ ny∈ C n are mutually absolutely continuous if and only if ℓ= n ℓ= n; they are singular
each other if and only if ℓ\not= n ℓ≠ n. Furthermore, we give an explicit expression of the
Radon–Nikodym density d G _ x/d G _ yd G x/d G y for x, y ∈ C^ ℓ x, y∈ C ℓ.
process GG and its reduced Palm measures {G _ x, x ∈ C^ ℓ, ℓ= 0, 1, 2 ...\} G x, x∈ C ℓ, ℓ= 0,
1, 2…, namely, reduced Palm measures G _ x G x and G _ y G y for x ∈ C^ ℓ x∈ C ℓ and y
∈ C^ ny∈ C n are mutually absolutely continuous if and only if ℓ= n ℓ= n; they are singular
each other if and only if ℓ\not= n ℓ≠ n. Furthermore, we give an explicit expression of the
Radon–Nikodym density d G _ x/d G _ yd G x/d G y for x, y ∈ C^ ℓ x, y∈ C ℓ.
Abstract
We prove a dichotomy between absolute continuity and singularity of the Ginibre point process and its reduced Palm measures , namely, reduced Palm measures and for and are mutually absolutely continuous if and only if ; they are singular each other if and only if . Furthermore, we give an explicit expression of the Radon–Nikodym density for .
Springer
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