Open Access
2018 Hole probabilities for $\beta $-ensembles and determinantal point processes in the complex plane
Kartick Adhikari
Electron. J. Probab. 23: 1-21 (2018). DOI: 10.1214/18-EJP176
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.

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Kartick Adhikari "Hole probabilities for $\beta $-ensembles and determinantal point processes in the complex plane," Electronic Journal of Probability 23(none), 1-21, (2018). https://doi.org/10.1214/18-EJP176
Received: 4 May 2017; Accepted: 7 May 2018; Published: 2018
Vol.23 • 2018
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