CONTINUOUS TIME RANDOM WALKS WITH MOMENTLESS WAITING TIME DISTRIBUTIONS

Continuous time random walk (CTRW) is studied in the case of momentless waiting time distributions with long-time tail t^-α, 0 < α < 1. It is found that the hopping event set is a well defined random fractal whose fractal (Hausdorff) dimension is α, and if one quantity of discrete time random walk R(n) e.g., S(n) the number of distinct sites visited up to step n has scaling exponent β > 0, then its corresponding quantity of CTRW R(T) (e.g., S ( t ) the number of distinct sites visited up to time t) has scaling exponent αβ.