Electronic Journal of Probability

Hole probabilities for $\beta $-ensembles and determinantal point processes in the complex plane

Kartick Adhikari

Full-text: Open access

Abstract

We compute the exact decay rate of the hole probabilities for $\beta $-ensembles and determinantal point processes associated with the Mittag-Leffler kernels in the complex plane. We show that the precise decay rate of the hole probabilities is determined by a solution to a variational problem from potential theory for both processes.

Article information

Source
Electron. J. Probab., Volume 23 (2018), paper no. 48, 21 pp.

Dates
Received: 4 May 2017
Accepted: 7 May 2018
First available in Project Euclid: 1 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1527818426

Digital Object Identifier
doi:10.1214/18-EJP176

Mathematical Reviews number (MathSciNet)
MR3814242

Zentralblatt MATH identifier
06924660

Subjects
Primary: 60G55: Point processes

Keywords
hole probability $\beta $-ensembles determinantal point processes weighted minimum energy weighted equilibrium measure balayage measure weighted Fekete points

Rights
Creative Commons Attribution 4.0 International License.

Citation

Adhikari, Kartick. Hole probabilities for $\beta $-ensembles and determinantal point processes in the complex plane. Electron. J. Probab. 23 (2018), paper no. 48, 21 pp. doi:10.1214/18-EJP176. https://projecteuclid.org/euclid.ejp/1527818426


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