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.
Citation
Kartick Adhikari. "Hole probabilities for $\beta $-ensembles and determinantal point processes in the complex plane." Electron. J. Probab. 23 1 - 21, 2018. https://doi.org/10.1214/18-EJP176
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