  Heat-transport mechanism mediated by near-field interactions in plasmonic
nanostructures networks is shown to be analogous to a generalized random-walk
process. Existence of superdiffusive regimes is demonstrated both in linear
ordered chains and in three dimensional random networks by analyzing the
asymptotic behavior of the corresponding probability distribution function. We
show that the spread of heat in these networks is described by a type of
L\'{e}vy flight. The presence of such anomalous heat transport regimes in
plasmonic networks opens the way to the design of a new generation of composite
materials able to transport heat faster than the normal diffusion process in
solids.
