  We compute and compare the decay lengths of several correlation functions and
effective coupling constants in the many-body localized (MBL) phase. To this
end, we consider the distribution of the logarithms of these couplings and
correlators: in each case the log-coupling follows a normal distribution with
mean and variance that grow linearly with separation. Thus, a localization
length is asymptotically sharply defined for each of these quantities. These
localization lengths differ numerically from one another, but all of them
remain short up to the numerically observed MBL transition, indicating
stability of the MBL phase against isolated ergodic inclusions. We also show
how these broad distributions may be extracted using interferometric probes
such as double electron-electron resonance (DEER) and the statistics of local
spin precession frequencies.
