Threshold behaviour of random resistor networks: a synthesis of theoretical approaches

Random resistor networks have been studied previously in several ways, including (i) the Cayley tree model, (ii) the Skal-Shklovskii-de Gennes 'nodes and chains' model, and (iii) position-space renormalisation. Here these approaches are combined, giving a clearer view of the roles of the nodes and chains, and a new explanation of the upper critical dimensionality.