Convective amplification in large homogeneous systems is studied, both analytically and numerically, in the case of a linear diffraction-free stochastic amplifier. Overall amplification does not result from successive amplifications in small scale high intensity hot spots, but from a single amplification in a delocalized mode of the driver field spreading over the whole interaction length. For this model, the hot-spot approach is found to systematically underestimate the gain factor by more than 50%.
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