  We consider the probability of having two intervals (gaps) without
eigenvalues in the bulk scaling limit of the Gaussian Unitary Ensemble of
random matrices. We describe uniform asymptotics for the transition between a
single large gap and two large gaps. For the initial stage of the transition,
we explicitly determine all the asymptotic terms (up to the decreasing ones) of
the logarithm of the probability. We obtain our results by analyzing
double-scaling asymptotics of a Toeplitz determinant whose symbol is supported
on two arcs of the unit circle.
