%0 Unpublished work
%T Determinantal point processes associated with Hilbert spaces of holomorphic functions
%+ Institut de MathÃ©matiques de Marseille (I2M)
%+ Institut de MathÃ©matiques de Toulouse UMR5219 (IMT)
%A Bufetov, Alexander I.
%A Qiu, Yanqi
%8 2016-01-14
%D 2016
%K Determinantal point processes
%K Palm measures
%K generalized Fock spaces
%K generalized Bergman spaces
%K regularized multiplicative functionals
%K rigidity
%Z Mathematics [math]/Dynamical Systems [math.DS]Preprints, Working Papers, ...
%X 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.
%G English
%2 https://hal.archives-ouvertes.fr/hal-01256224/document
%2 https://hal.archives-ouvertes.fr/hal-01256224/file/DPP-Berg.pdf
%L hal-01256224
%U https://hal.archives-ouvertes.fr/hal-01256224
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