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The blazar Mrk 421 is one of the closest, brightest and fastest varyingsource in the extragalactic X-ray/TeV sky. In the last years, manymulti-wavelength campaigns have been carried out to study the correlationbetween the very high energy (VHE) $\gamma$-ray and X-ray fluxes of this sourceand, although the activity in these two energy ranges seems to be correlated inmany observations, no conclusive results have been achieved yet. In this workwe present a robust study of the VHE $\gamma$-ray/X-ray correlation of Mrk 421with data taken with different VHE experiments on different time scales and fordifferent levels of activity of the source, with special focus on the lowactivity states. In particular, we discuss the robustness of the correlation atthe lowest fluxes corresponding to the quiescent state of Mrk 421.

VHE $\gamma$-ray/X-ray correlation studies in Mrk 421 down to the quiescent state