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Front propagation in a random environment is studied close to the depinningthreshold. At zero temperature we show that the depinning force distributionexhibits a universal behavior. This property is used to estimate the velocityof the front at very low temperature. We obtain a Arrhenius behavior with aprefactor depending on the temperature as a power law. These results aresupported by numerical simulations.Comment: 6 pages, 2 figures, accepted in Int. J. Mod. Phys.

FRONT PROPAGATION IN RANDOM MEDIA: FROM EXTREMAL TO ACTIVATED DYNAMICS