  We consider two models of one-dimensional random walks among biased i.i.d.
random conductances: the first is the classical exponential tilt of the
conductances, while the second comes from the effect of adding an external
field to a random walk on a point process (the bias depending on the distance
between points). We study the case when the walk is transient to the right but
sub-ballistic, and identify the correct scaling of the random walk: we find
$\alpha \in[0,1]$ such that $\log X_n / \log n \to \alpha$. Interestingly,
$\alpha$ does not depend on the intensity of the bias in the first case, but it
does in the second case.
