Random walks on percolation structures
Random walks on percolation structures
In this chapter another, experimentally widespread, situation is considered. The random walk takes place not on a homogeneous lattice, where each site in principle accessible to the walker, but on a percolation structure where some sites are not accessible. Close to the percolation threshold, when the system of accessible sites disintegrates into finite clusters, and the connected way through the whole lattice does not exist anymore, the properties of the corresponding walks are related to the fractal structure of the infinite cluster and are quite unusual. The chapter discusses some basic notions of fractal geometry, the properties of random walks on such structures and their effects on the kinetics of simple reactions in percolation systems. The case when the walker can start at an infinite as well as at a finite cluster is also considered.
Keywords: percolation transition, fractals, fractal dimension, random walks on fractals, spectral dimension, role of finite clusters
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