  We have measured the center-of-mass fluctuations of the height of a contact
line at depinning for two different systems: liquid hydrogen on a rough cesium
substrate and isopropanol on a silicon wafer grafted with silanized patches.
The contact line is subject to a confining quadratic well, provided by gravity.
  From the second cumulant of the height fluctuations, we measure the
renormalized disorder correlator Delta(u), predicted by the Functional RG
theory to attain a fixed point, as soon as the capillary length is large
compared to the Larkin length set by the microscopic disorder. The experiments
are consistent with the asymptotic form for Delta(u) predicted by Functional
RG, including a linear cusp at u=0. The observed small deviations could be used
as a probe of the underlying physical processes. The third moment, as well as
avalanche-size distributions are measured and compared to predictions from
Functional RG.
