ANTIRED BONDS DISTRIBUTION LAW IN 3D PERCOLATION

Combining two independent approaches the power law structure of the anti-red bonds distribution in d = 3 percolation can be derived. This result is important to understand the dynamical behaviour of fluctuating fronts during diffusion and invasion processes, but also in problems of fragmentation-aggregation of percolation clusters. In d = 2, it allows to calculate the fractal dimension of the hull, D(h) = 1 + 1/nu, a known result not easy to prove. In d > 2 dimensions, it gives an anti-red bonds equal to D(anti-red) = 2D - 1/nu - d.