We study the role of noise in the propagation of a front into an unstable medium, as described by a Langevin equation for a scalar field. We investigate the crossover that occurs between constant-velocity propagation at early times and diffusive behavior at late times. We show that the time at which this crossover occurs is strongly correlated with the growth of the local value of the order parameter in the unstable region ahead of the front. We discuss the implications of our results concerning the relevance of noise terms in nonequilibrium problems involving spatial inhomogeneities.
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