Scaling properties of pinned interfaces in fractal media

It is well established that for sufficiently strong driving, the interface feels an effective smeared out thermal noise and its fluctuations present all the typical phenomena of scale invariance of driven systems. In the opposite case of weak driving, the quenched nature of spatial heterogeneities becomes apparent and the interface reaches a pinned state, characterized by completely different roughness exponents. This paper aims to understand the effect of long-range correlations in fractal media on the scaling properties of pinned interfaces.