  The study of short-term variability properties in AGN jets has the potential
to shed light on their particle acceleration and emission mechanisms. We report
results from a four-day coordinated multi-wavelength campaign on the
highly-peaked blazar (HBL) Mkn 421 in 2019 January. We obtained X-ray data from
AstroSAT, BVRI photometry with the Whole Earth Blazar Telescope (WEBT), and TeV
data from FACT to explore short-term multi-wavelength variability in this HBL.
The X-ray continuum is rapidly variable on time-scales of tens of ks.
Fractional variability amplitude increases with energy across the synchrotron
hump, consistent with previous studies; we interpret this observation in the
context of a model with multiple cells whose emission spectra contain cutoffs
that follow a power-law distribution. We also performed time-averaged and
time-resolved (time-scales of 6 ks) spectral fits; a broken power-law model
fits all spectra well; time-resolved spectral fitting reveals the usual
hardening when brightening behaviour. Intra-X-ray cross correlations yield
evidence for the 0.6-0.8 keV band to likely lead the other bands by an average
of 4.6 +- 2.6 ks, but only during the first half of the observation. The source
displayed minimal night-to-night variability at all wavebands thus precluding
significant interband correlations during our campaign. The broadband SED is
modeled well with a standard one-zone leptonic model, yielding jet parameters
consistent with those obtained from previous SEDs of this source.
