1306.0216 (Jinho Baik)

Circular unitary ensemble with highly oscillatory potential    [PDF]

Jinho Baik

We study the effect of a highly oscillatory potential to the eigenvalues of a random matrix. Consider the circular unitary ensembles with an external potential which is periodic with the period comparable to the average spacings of the eigenvalues. We show that in this case the density of states is periodic and does not converge in the large matrix limit, but the local correlation function converges to a simple combination of the sine kernel and the potential. We evaluate the correlation function exactly and also asymptotically.

View original: http://arxiv.org/abs/1306.0216