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Abstract
A brief summary of recent results obtained by the renormalization-group ϵ-expansion (ϵ = 6−d, where d is the spatial dimension) and by low-concentration series for resistive correlations in random structures is presented. Most results refer to percolating clusters, but some results for random and self-avoiding walks are included. Results are presented for (a) the cross-over exponent φ for the two-point resistance for linear and nonlinear networks, where v is the correlation length exponent for percolation and [·]av denotes a percolation average; (b) φ for the Swiss-cheese model; (c) the generalized noise or current distribution exponents Ψq, defined by Where Σbib(x,x′) is the current in the bond b when a unit current is injected at x and removed at x′(d) amplitude ratios for various combinations of resistive and diffusional susceptibilities; (e) moments of diffusion times for both blind and myopic ants in terms of resistive correlations; and (f) resistive properties of random and self-avoiding walks.