Derivation of the Continuous-Time Random-Walk Equation

Abstract
The transport of electrons or excitations on a lattice randomly occupied by guests is considered. The equation governing the transport in any configuration is assumed to be the master equation. A projection operator technique is used to derive the exact equation governing the transport averaged over all configurations, which can be written as either a generalized master equation or the continuous-time random-walk equations (CTRW), establishing the correctness of the CTRW for these problems.