Motivated by the desire to model internet traffic we consider random walks that start and are absorbed on the leaves of random networks and study the length of such walks. We present and test two techniques to analyse these walks. On Erdős–Rényi random graphs where the probability of a walk...

The disturbance of the transmission of a diffusive medium due to an object hidden in it can be expressed in terms of an effective charge and dipole moment. In the mesoscopic regime, beyond the diffusion approximation, we calculate this effective charge and dipole moment. Various objects are...