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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 $U$.
The gamma kernels are a family of projection kernels $K^{(z,z)}=K^{(z,z)}(x,y)$ on a doubly infinite $1$-dimensional lattice. They are expressed through Eulers gamma function and depend on two continuous parameters $z,z$. The gamma kernels initially
We show that the central limit theorem for linear statistics over determinantal point processes with $J$-Hermitian kernels holds under fairly general conditions. In particular, We establish Gaussian limit for linear statistics over determinantal poin
We show that the symplectic and orthogonal character analogues of Okounkovs Schur measure (on integer partitions) are determinantal, with explicit correlation kernels. We apply this to prove certain Borodin-Okounkov-Gessel-type results concerning Toe
For a Pfaffian point process we show that its Palm measures, its normalised compositions with multiplicative functionals, and its conditional measures with respect to fixing the configuration in a bounded subset are Pfaffian point processes whose kernels we find explicitly.
Determinantal point processes (DPPs) are popular probabilistic models of diversity. In this paper, we investigate DPPs from a new perspective: property testing of distributions. Given sample access to an unknown distribution $q$ over the subsets of a