  The conditions for the appearance of a sharp laser transition are formulated
in terms of a scaling limit, involving vanishing cavity loss and light-matter
coupling, $\kappa \to 0$, $g \to 0$, such that $g^2/\kappa$ stays finite. It is
shown analytically that in this asymptotic parameter domain, and for pump rates
above the threshold value, the photon output becomes large in a sense that is
specified, and the photon statistics becomes strictly Poissonian. Numerical
examples for the case of a two-level and a three-level emitter are presented
and discussed in relation to the analytic result.
