5.5 years multi-wavelength variability of Mrk 421: evidences of leptonic
  emission from the radio to TeV
  Mrk 421 is a high-synchrotron-peaked blazar featuring bright and persistent
GeV and TeV emission. We use the longest and densest ongoing unbiased observing
campaign obtained at TeV and GeV energies during 5.5 years with the FACT
telescope and the Fermi-LAT detector. The contemporaneous multi-wavelength
observations were used to characterize the variability of the source and to
constrain the underlying physical mechanisms. We study and correlate light
curves obtained by nine different instruments from radio to gamma rays and
found two significant results. The TeV and X-ray light curves are very well
correlated with lag, if any, shorter than a day. The GeV light curve varies
independently and accurately leads the variations observed at long wavelengths,
in particular in the radio band. We find that the observations match the
predictions of leptonic models and suggest that the physical conditions vary
along the jet, when the emitting region moves outwards.
