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The motion of self-propelled particles is modeled as a persistent randomwalk. An analytical framework is developed that allows the derivation of exactexpressions for the time evolution of arbitrary moments of the persistentwalk's displacement. It is shown that the interplay of step length and turningangle distributions and self-propulsion produces various signs of anomalousdiffusion at short time scales and asymptotically a normal diffusion behaviorwith a broad range of diffusion coefficients. The crossover from the anomalousshort time behavior to the asymptotic diffusion regime is studied and theparameter dependencies of the crossover time are discussed. Higher moments ofthe displacement distribution are calculated and analytical expressions for thetime evolution of the skewness and the kurtosis of the distribution arepresented.

Persistent-random-walk approach to anomalous transport of self-propelled particles