  We study the effect of randomly distributed diffusivities and speeds in two
models for active particle dynamics with active and passive fluctuations. We
demonstrate how non-Gaussian displacement distributions emerge in these models
in the long time limit, including Cauchy-type and exponential (Laplace) shapes.
Notably the resulting shapes of the displacement distributions with distributed
diffusivities for the active models considered here are in striking contrast to
passive diffusion models. For the active motion models our discussion points
out the differences between active- and passive-noise. Specifically, we
demonstrate that the case with active-noise is in nice agreement with measured
data for the displacement distribution of social amoeba.
