Current and voltage distributions in resistor network with a broad distribution of conductances

Random resistor networks with bonds occupied randomly by conductances g = e xp (-lambda x), where x is the random variable on [0, 1] and lambda much gr eater than 1 are investigated by means of numerical simulations. The proble m of correlation between local conductance and local current or local volta ge is addressed. The distributions of currents, voltages and power dissipat ed are calculated for separate subsets of bonds with identical value of con ductance. It occurs that subsets of highly/poorly conductive bonds have ide ntical distributions of currents/voltages. From this we conclude that withi n the subset of highly/poorly conducting bonds local conductance and local current/voltage are statistically independent variables.