The sine process is a rigid point process on the real line, which means that
for almost all configurations X, the number of points in an interval I=[−R,R] is determined by the points of X outside of I. In addition, the
points in I are an orthogonal polynomial ensemble on I with a weight
function that is determined by the points in X∖I. We prove a
universality result that in particular implies that the correlation kernel of
the orthogonal polynomial ensemble tends to the sine kernel as the length
∣I∣=2R tends to infinity, thereby answering a question posed by A.I. Bufetov.Comment: 26 pages, no figures, revised version with Appendix