Markov matrix analysis of random walks in disordered continuous media

We study by a Markov matrix analysis of the equivalent random walks the dynamic properties of continuous media consisting of both correlated and uncorrelated equal-size spheres. We employ a blind ant random-walk model using the rule that a walker jumps among centers of the directly connected spherical particles on an infinite network. The dominant eigenvalues and eigenvectors of the transition probability matrix of the random walks are calculated, yielding estimates of the spectral dimension ds and the fractal dimension dw of random walks on the continuous network. We find that, for the present model, the estimates are very close to the corresponding lattice percolation values, though only after the finite-size effects have been carefully taken into account. We also show that the finite-size scaling of the largest nontrivial eigenvalues holds for our model with the same exponents as for the lattice percolation.