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We point out that the celebrated GRW master-equation is invariant undertranslations, reflecting the homogeneity of space, thus providing a particularrealization of a general class of translation-covariant Markovianmaster-equations. Such master-equations are typically used for the descriptionof decoherence due to momentum transfers between system and environment.Building on this analogy we show the exact relationship between the GRWmaster-equation and decoherence master-equations, further providing acollisional decoherence model formally equivalent to the GRW master-equation.This allows for a direct comparison of order of magnitudes of relevantparameters. This formal analogy should not lead to confusion on the utterlydifferent spirit of the two research fields, in particular it has to bestressed that the decoherence approach does not lead to a solution of themeasurement problem. Building on this analogy however the feasibility of theextension of spontaneous localization models in order to avoid the infiniteenergy growth is discussed. Apart from a particular case considered in thepaper, it appears that the amplification mechanism is generally spoiled by suchmodifications.Comment: 9 pages, latex, no figures, to appear on J. Phys.

On the precise connection between the GRW master equation and master equations for the description of decoherence