Blaschke products and Palm distributions of the determinantal point process with the Bergman kernel

Alexander I. Bufetov, Yanqi Qiu

Published 2014-11-18Version 1

The main result of this note, Theorem 2.7, gives explicit formulae for the Radon-Nikodym derivatives between the reduced Palm distributions, of all orders, for the determinantal point process with the Bergman kernel on the unit disk, the point process describing zeros of the i.i.d. Gaussian power series. The Radon-Nikodym derivatives are expressed as regularized multiplicative functionals related to Blaschke products. Our computation gives a new proof of the equivalence of the reduced Palm distributions of this determinantal point process, established by Holroyd and Soo. As a corollary, in Theorem 3.2 we establish the quasi-invariance of this determinantal point process, under the action of the group of diffeomorphisms with compact support in the open unit disk.