CONTINUOUS TIME RANDOM WALKS ON FRACTALS: RIGOROUS RESULTS

Continuous time random walk on fractals is studied Asymptotic forms of < r²(t)>, S(t ) and P(t) are obtained rigorously by the generalized Blackwell theorem, where < r²(t) > is the mean-square displacement, S(t) the number of distinct sites visited in time t, and P(t) the probability of return at time t. The spatial disorder turns out to be predominant for long time.