Overcrowding asymptotics for the Sine_beta process
Abstract
We give overcrowding estimates for the Sine_beta process, the bulk point process limit of the Gaussian betaensemble. 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.
 Publication:

arXiv eprints
 Pub Date:
 June 2015
 arXiv:
 arXiv:1506.07117
 Bibcode:
 2015arXiv150607117H
 Keywords:

 Mathematics  Probability;
 Mathematical Physics
 EPrint:
 20 pages, no figures