Open Access
Translator Disclaimer
March 2018 Quasi-symmetries of determinantal point processes
Alexander I. Bufetov
Ann. Probab. 46(2): 956-1003 (March 2018). DOI: 10.1214/17-AOP1198


The main result of this paper is that determinantal point processes on $\mathbb{R}$ corresponding to projection operators with integrable kernels are quasi-invariant, in the continuous case, under the group of diffeomorphisms with compact support (Theorem 1.4); in the discrete case, under the group of all finite permutations of the phase space (Theorem 1.6). The Radon–Nikodym derivative is computed explicitly and is given by a regularized multiplicative functional. Theorem 1.4 applies, in particular, to the sine-process, as well as to determinantal point processes with the Bessel and the Airy kernels; Theorem 1.6 to the discrete sine-process and the Gamma kernel process. The paper answers a question of Grigori Olshanski.


Download Citation

Alexander I. Bufetov. "Quasi-symmetries of determinantal point processes." Ann. Probab. 46 (2) 956 - 1003, March 2018.


Received: 1 October 2015; Revised: 1 May 2017; Published: March 2018
First available in Project Euclid: 9 March 2018

zbMATH: 06864077
MathSciNet: MR3773378
Digital Object Identifier: 10.1214/17-AOP1198

Primary: 60G55
Secondary: 22E66 , 33C10 , 60B10 , 60B15

Keywords: Determinantal point processes , Gibbs property , integrable kernels , multiplicative functionals , Palm measures

Rights: Copyright © 2018 Institute of Mathematical Statistics


Vol.46 • No. 2 • March 2018
Back to Top