We consider the entropy of systems of random transformations, where the transformations are chosen from a set of generators of a Z d action. We show that the classical denition gives unsatisfactory entropy results in the higher-dimensional case, i.e. when d 2. We propose a denition of the entropy for random group actions which agrees with the classical denition in the one-dimensional case, and which gives satisfactory results in higher dimensions. This denition is based on the bre entropy of a certain skew product. We identify the entropy by an explicit formula which makes it possible to compute the entropy in certain cases
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