  As a function of the driving strength, a degenerate parametric oscillator
exhibits an instability at which spontaneous oscillations occur. Close to
threshold, both the nonlinearity as well as fluctuations are vital to the
accurate description of the dynamics. We study the statistics of the radiation
that is emitted by the degenerate parametric oscillator at threshold. For a
weak nonlinearity, we can employ a quasiclassical description. We identify a
universal Liouvillian that captures the relevant long-time dynamics for large
photon-numbers. We find that the cumulants obey a universal power-law scaling
as a function of the nonlinearity. The Fano factor shows a maximum close, but
not coinciding, with the threshold. Moreover, we predict a certain ratio of the
first three cumulants to be independent of the microscopic details of the
system and connect the results to experimental platforms.
