On the validity of the independent hot-spot model

The results of the independent hot-spot (IHS) model are compared to those of the underlying stochastic amplifier in the regime where the coupling of the amplifier is close to its critical value. The considered case is that of a 1D linear amplifier with at most one hot spot per interaction length. It is shown that the validity of the critical coupling given by the IHS model depends on the correlation function of the pump field and should be discussed in each particular case. The discrepancy between the IHS model and the underlying amplifier is shown to be due to the random fluctuations of the hot-spot field around its dominant, deterministic, component.