On scaling relations in growth models for percolating clusters and diffusion fronts

Employing analogies between the growth of the incipient percolating cluster and the growth of a diffusion front, the authors develop a scaling theory for this latter model. Their scaling assumptions support the Sapoval-Rosso-Gouyet conjecture, dH=1+1/ nu , which relates, in two dimensions, the fractal dimension dH of the hull of the incipient percolating cluster to the correlation length exponent nu in percolation, and yield relations between the static and dynamic exponents of the growth of a diffusion front.