# Overcrowding asymptotics for the Sine_beta process

@article{Holcomb2015OvercrowdingAF, title={Overcrowding asymptotics for the Sine\_beta process}, author={D. Holcomb and Benedek Valk'o}, journal={arXiv: Probability}, year={2015} }

We give overcrowding estimates for the Sine_beta process, the bulk point process limit of the Gaussian beta-ensemble. We show that the probability of having at least n points in a fixed interval is given by $e^{-\frac{\beta}{2} n^2 \log(n)+O(n^2)}$ as $n\to \infty$. We also identify the next order term in the exponent if the size of the interval goes to zero.

#### One Citation

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We investigate Sine$_\beta$, the universal point process arising as the thermodynamic limit of the microscopic scale behavior in the bulk of one-dimensional log-gases, or $\beta$-ensembles, at… Expand

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