  The responses of a $1+\epsilon $ dimensional directed path to temperature and
to potential variations are calculated exactly, and are governed by the same
scaling form. The short scale decorrelation (strong correlation regime) leads
to the overlap length predicted by heuristic approaches; its temperature
dependence and large absolute value agree with scaling and numerical
observations. Beyond the overlap length (weak correlation regime), the
correlation decays algebraically. A clear physical mechanism explains the
behavior in each case: the initial decorrelation is due to `fragile droplets,'
which contribute to the entropy fluctuations as $\sqrt{T}$, while the residual
correlation results from accidental intersections of otherwise uncorrelated
configurations.
