DIFFUSION AND SPECTRAL DIMENSION ON EDEN TREE

We calculate the eigenspectrum of random walks on the Eden tree in two and three dimensions. From this, we calculate the spectral dimension d(s) and the walk dimension d(w) and test the scaling relation d(s)=2d (f)/d(w) (=2d/d(w) for an Eden tree). Finite-size induced crossovers a re observed, whereby the system crosses over from a short-time regime where this relation is violated (particularly in two dimensions) to a long-time regime where the behaviour appears to be complicated and dep endent on dimension, even qualitatively.