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We have measured the center-of-mass fluctuations of the height of a contactline at depinning for two different systems: liquid hydrogen on a rough cesiumsubstrate 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 therenormalized disorder correlator Delta(u), predicted by the Functional RGtheory to attain a fixed point, as soon as the capillary length is largecompared to the Larkin length set by the microscopic disorder. The experimentsare consistent with the asymptotic form for Delta(u) predicted by FunctionalRG, including a linear cusp at u=0. The observed small deviations could be usedas a probe of the underlying physical processes. The third moment, as well asavalanche-size distributions are measured and compared to predictions fromFunctional RG.

Height fluctuations of a contact line: a direct measurement of the renormalized disorder correlator