Distribution of the logarithms of currents in percolating resistor networks. I. Theory
Distribution of the logarithms of currents in percolating resistor networks. I. Theory
The distribution of currents, ${\mathit{i}}_{\mathit{b}}$, in the bonds b of a randomly diluted resistor network at the percolation threshold is investigated through a study of the moments of the distribution P^(${\mathit{i}}^{2}$) and the moments of the distribution P(y), where y=-ln${\mathit{i}}_{\mathit{b}}^{2}$. For q>${\mathit{q}}_{\mathit{c}}$ the qth moment of P^(${\mathit{i}}^{2}$), ${\mathit{M}}_{\mathit{q}}$ (i.e., the …