  We introduce a new approach to connectivity-dependent properties of diluted
systems, which is based on the transfer-matrix formulation of the percolation
problem. It simultaneously incorporates the connective properties reflected in
non-zero matrix elements and allows one to use standard random-matrix
multiplication techniques. Thus it is possible to investigate physical
processes on the percolation structure with the high efficiency and precision
characteristic of transfer-matrix methods, while avoiding disconnections. The
method is illustrated for two-dimensional site percolation by calculating (i)
the critical correlation length along the strip, and the finite-size
longitudinal DC conductivity: (ii) at the percolation threshold, and (iii) very
near the pure-system limit.
