, The map M (T

, S i )). For example, if some strips S i have a non

, The proof of Proposition 5.6 from Lemma 5.7 is very similar, as well as points (i) and (ii) of Lemma 5.7. The only difference is that the proof of point (ii) of Lemma 5.7 is easier in our new framework, because of the independence of the strips, and we do not need anymore to restrict ourselves to even values of k. Exactly as in the first proof, by using the "self-similarity" property of S (T, (S i ) i?0 ), the proof of point (iii) of Lemma 5.7 can be reduced to the proof that the dual map of S (T, (S i ) i?0 ) is transient (it is also important that the sets A k do not touch each other, which is why we have required that the boundaries of the strips are simple). The adaptation of the proof of Lemma 5.10 (transience of the dual slice), however, is not obvious, particular, we choose for (x n ) a nonbacktracking random walk on T, and the sets A k are built in the same way as in the original proof, but from T instead of B(T )

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