Non-Gaussian properties of transport in active systems

Appearance of non-Gaussian features for transport in systems with active elements becomes less an exception but rather a rule. Examples include transport mediated by molecular motors and diffusion in a bacteria suspension. Experimentally obtained single particle trajectories reveal presence of prolonged jumps, an effect that is frequently attributed to active processes, e.g. adherence of a bead to a moving bacteria. Number of such "active" events fluctuates from one trajectory to another. We present a simple model of a random walk with random number of jumps. Analytically obtained results show that non-Gaussian features, like exponential decay of the displacement probability density function, naturally appear in the model. Moreover the model predicts that close to exponential behavior of the tails of the displacement distribution is an attractor for a wide class of systems.