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We consider a random walk in an i.i.d. random environment on Z that isperturbed by cookies of strength 1. The number of cookies per site is assumedto be i.i.d. Results on the speed of the random walk are obtained. Our maintool is the correspondence in certain cases between the random walk and abranching process in a random environment with migration.

On the speed of a one-dimensional random walk in a random environment perturbed by cookies of strength one