Non-Gaussian displacement distributions in models of heterogeneous active particle dynamics

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 asymptotic behaviours of such Cauchy shapes are universal and do not depend on the precise diffusivity distributions. Moreover, 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.

Automated summary

We study the effects of randomly distributed diffusivities and speeds in two models for active particle dynamics. We find that non-Gaussian displacement distributions, including Cauchy-type and exponential shapes, emerge in these models in the long time limit. The resulting shapes of the displacement distributions with distributed diffusivities for the active models are in striking contrast to passive diffusion models. Additionally, we demonstrate that the case with active-noise agrees well with measured data for the displacement distribution of social amoeba.