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Random Walks in I.I.D. Random Environment on Cayley Trees
**

**Abstract :**
We consider the random walk in an *i.i.d.* random environment on the infinite d-regular tree for
d ≥ 3. We consider the tree as a Cayley graph of free product of finitely many copies of ℤ
and ℤ_{2} and define the i.i.d. environment as invariant under the action of this group.
Under a mild non-degeneracy assumption we show that the walk is always transient.