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Random walks on GW-trees (transformation)

mathbb{E}_{e_*}[|X_{k+1}|-|X_k| \ | \mathcal{S}]=\sum_{k=0}^{n-1}\mathbb{E}_{e_*}[\frac{\nu(X_k)-\lambda}{\nu(X_k)+\lambda} \ | \mathcal{S}]$ $\mathcal{S}$ is here the survival set and $\mathbb{E}$ the expectation
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