Determinantal point processes associated with Hilbert spaces of holomorphic functions

Abstract : We study determinantal point processes on C induced by the reproducing kernels of generalized Fock spaces as well as those on the unit disc D induced by the reproducing kernels of generalized Bergman spaces. In the first case, we show that all reduced Palm measures of the same order are equivalent. The Radon-Nikodym derivatives are computed explicitly using regularized multiplicative functionals. We also show that these determinantal point processes are rigid in the sense of Ghosh and Peres, hence reduced Palm measures of different orders are singular. In the second case, we show that all reduced Palm measures, of all orders, are equivalent. The Radon-Nikodym derivatives are computed using regularized multiplicative function-als associated with certain Blaschke products. The quasi-invariance of these deter-minantal point processes under the group of diffeomorphisms with compact supports follows as a corollary.
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Pré-publication, Document de travail
2016
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https://hal.archives-ouvertes.fr/hal-01256224
Contributeur : Alexander I. Bufetov <>
Soumis le : jeudi 14 janvier 2016 - 15:10:54
Dernière modification le : mercredi 12 décembre 2018 - 15:17:26
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  • HAL Id : hal-01256224, version 1

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Alexander I. Bufetov, Yanqi Qiu. Determinantal point processes associated with Hilbert spaces of holomorphic functions. 2016. 〈hal-01256224〉

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