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

Abstract

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 $U$.

31 pages

References in corpus (1)

• Rigidity and Tolerance in Gaussian zeroes and Ginibre eigenvalues: quantitative estimates