We describe how one can obtain the pair correlation function of the Sine-beta process for beta=2n using the random operator framework. Our method recovers the classical formulas for beta=2 and 4. For general beta=2n, we identify the pair correlation function in terms of an ODE system, and also in terms of a matrix-valued generalization of hypergeometric functions. 
 
Joint with Yahui Qu (UW–Madison).