## Electronic Journal of Probability

### The random matrix hard edge: rare events and a transition

Diane Holcomb

#### Abstract

We study properties of the point process that appears as the local limit at the random matrix hard edge. We show a transition from the hard edge to bulk behavior and give a central limit theorem and large deviation result for the number of points in a growing interval $[0,\lambda ]$ as $\lambda \to \infty$. We study these results for the square root of the hard edge process. In this setting many of these behaviors mimic those of the $\mathrm{Sine} _\beta$ process.

#### Article information

Source
Electron. J. Probab., Volume 23 (2018), paper no. 85, 20 pp.

Dates
Accepted: 10 August 2018
First available in Project Euclid: 12 September 2018

https://projecteuclid.org/euclid.ejp/1536717744

Digital Object Identifier
doi:10.1214/18-EJP212

Mathematical Reviews number (MathSciNet)
MR3858913

Zentralblatt MATH identifier
06964779

#### Citation

Holcomb, Diane. The random matrix hard edge: rare events and a transition. Electron. J. Probab. 23 (2018), paper no. 85, 20 pp. doi:10.1214/18-EJP212. https://projecteuclid.org/euclid.ejp/1536717744

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