Multiple peaks in the displacement distribution of active random walkers

We consider a simple model for active random walk with general temporal correlations, and investigate the shape of the probability distribution function of the displacement during a short time interval. We find that under certain conditions the distribution exhibits multiple peaks and we show analytically and numerically that the existence of these peaks is governed by the walker's tendency to move forward, while the correlations between the timing of its active motion control the magnitude and shape of the peaks. In particular, we find that in a homogeneous system such peaks can occur only if the persistence is strong enough.