Properties of the density relaxation function in classical diffusion models with percolation transition

The relation between the density relaxation function Phi and the pair connectedness is shown. Static and dynamical scaling for Phi and quantities related to it are derived from percolation scaling theory. Due to finite clusters Phi contains a non-ergodic singularity even in the conducting phase, whence a Green-Kubo identity does not hold. The form factor of this singularity is discussed. For d>or=3 the static polarisability can be related to a diverging characteristic length also above the threshold. Contributions come from confinement in finite clusters and from the structure of the infinite cluster.