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For a determinantal point process induced by the reproducing kernel of the weighted Bergman space \(A^2(U, \omega )\) over a domain \(U \subset \mathbb {C}^d\), we establish the mutual absolute continuity of reduced Palm measures of any order provided that the domain U contains a non-constant bounded holomorphic function. The result holds in all dimensions. The argument uses the \(H^\infty (U)\)-module structure of \(A^2(U, \omega )\). A corollary is the quasi-invariance of our determinantal point process under the natural action of the group of compactly supported diffeomorphisms of U.

Equivalence of Palm measures for determinantal point processes governed by Bergman kernels