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Accepted for publication in Annales I.H.P., Probabilites et StatistiquesInternational audienceWe prove the Einstein relation, relating the velocity under a small perturbation to the diffusivity in equilibrium, for certain biased random walks on Galton--Watson trees. This provides the first example where the Einstein relation is proved for motion in random media with arbitrary deep traps

Einstein relation for biased random walk on Galton–Watson trees