We study the probability that a real stationary Gaussian process has at least
ηT zeros in [0,T] (overcrowding), or at most this number
(undercrowding). We show that if the spectral measure of the process is
supported on ±[B,A], overcrowding probability transitions from exponential
decay to Gaussian decay at η=πA​, while undercrowding
probability undergoes the reverse transition at η=πB​.Comment: 17 page