# The stochastic Airy operator at large temperature

@article{Dumaz2019TheSA, title={The stochastic Airy operator at large temperature}, author={Laure Dumaz and Cyril Labb'e}, journal={arXiv: Probability}, year={2019} }

It was shown in [J. A. Ramirez, B. Rider and B. Virag. J. Amer. Math. Soc. 24, 919-944 (2011)] that the edge of the spectrum of $\beta$ ensembles converges in the large $N$ limit to the bottom of the spectrum of the stochastic Airy operator. In the present paper, we obtain a complete description of the bottom of this spectrum when the temperature $1/\beta$ goes to $\infty$: we show that the point process of appropriately rescaled eigenvalues converges to a Poisson point process on $\mathbb{R…

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