Tunneling and hoping are not exactly the same mechanisms. Tunneling occurs as soon as 2 fillers are separated by a very thin layer of insulating material (typically a few nm thick), because the probability of presence of an electron has a  not-so-narrow distribution, i.e. is not a Dirac. Therefore, the "tail" of the distribution easily penetrates into the insulating barrier, and the electron thus has a non-zero probability of crossing this barrier. Hence conduction may occur between fillers which are not in true physical contact. Whereas tunneling is a coherent process in which electrons move from one site to another, maintaining a definite phase relationship between the amplitudes, hopping is an incoherent, thermally activated process in which an electron moves from one site to another but loses all information about its phase in the process. A rather common conduction process (but not the only one) is for example the variable-range hopping (VRH) process. In VRH, the electrons "choose" the optimum between short hops (in terms of length) and "high" hops (in terms of energy). In 3D composites, this mechanism is revealed if plotting the log of the conductivity versus temperature at the power of -1/4 leads to a straight line. This is known as Mott's law. Tunneling leads to a different law of conductivity versus temperature.

Alain