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Equivalence of Palm measures for determinantal point processes governed by Bergman kernels (1703.08978v1)
Published 27 Mar 2017 in math.PR, math-ph, math.DS, math.FA, and math.MP
Abstract: For a determinantal point process induced by the reproducing kernel of the weighted Bergman space $A2(U, \omega)$ 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 $A2(U, \omega)$. A corollary is the quasi-invariance of our determinantal point process under the natural action of the group of compactly supported diffeomorphisms of $U$.