  Different classes of low-dimensional superconducting systems exhibit an
inhomogeneous filamentary superconducting condensate whose macroscopic
coherence still needs to be fully investigated and understood. Here we present
a thorough analysis of the superfluid response of a prototypical filamentary
superconductor embedded in a {two-dimensional} metallic matrix. By mapping the
system into an exactly solvable random impedance network, we show how the
dissipative (reactive) response of the system non-trivially depends on both the
macroscopic and microscopic characteristics of the metallic (superconducting)
fraction. We compare our calculations with resonant-microwave transport
measurements performed on LaAlO$_3$/SrTiO$_3$ heterostructures over an extended
range of temperatures and carrier densities finding that the filamentary
character of superconductivity accounts for unusual peculiar features of the
experimental data.
