Electronic Communications in Probability

Rigidity of the $\operatorname{Sine} _{\beta }$ process

Chhaibi Reda and Joseph Najnudel

Full-text: Open access

Abstract

We show that the $\operatorname{Sine} _{\beta }$ point process, defined as the scaling limit of the Circular Beta Ensemble when the dimension goes to infinity, and generalizing the determinantal sine-kernel process, is rigid in the sense of Ghosh and Peres: the number of points in a given bounded Borel set $B$ is almost surely equal to a measurable function of the position of the points outside $B$.

Article information

Source
Electron. Commun. Probab., Volume 23 (2018), paper no. 94, 8 pp.

Dates
Received: 26 May 2018
Accepted: 16 November 2018
First available in Project Euclid: 18 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1545102490

Digital Object Identifier
doi:10.1214/18-ECP195

Mathematical Reviews number (MathSciNet)
MR3896832

Zentralblatt MATH identifier
07023480

Subjects
Primary: 60G55: Point processes 60G57: Random measures 60K99: None of the above, but in this section

Keywords
the sine$_\beta $ point process rigidity of point processes random matrices

Rights
Creative Commons Attribution 4.0 International License.

Citation

Reda, Chhaibi; Najnudel, Joseph. Rigidity of the $\operatorname{Sine} _{\beta }$ process. Electron. Commun. Probab. 23 (2018), paper no. 94, 8 pp. doi:10.1214/18-ECP195. https://projecteuclid.org/euclid.ecp/1545102490


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