Non-Gaussianity and Dynamical Trapping in Locally Activated Random Walks

Olivier Benichou (1) , Nicolas Meunier (2) , Sidney Redner (3) , Raphael Voituriez (1)

1 LPTMC - Laboratoire de Physique Théorique de la Matière Condensée
2 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
3 Center for Polymer Studies

We propose a minimal model of locally activated random walks, in which the diffusion coefficient of a one-dimensional Brownian particle is modified in a prescribed way -- either increased or decreased -- upon each crossing of the origin. Importantly, the case of a local decrease of the motion ability is at work in the process of formation of the atherosclerotic plaque, when describing the dynamics of a macrophage cell that grows when accumulating localized lipid particles. We show in the general case that localized perturbations have remarkable consequences on the dynamics of the diffusion process at all scales, such as the emergence of a non-Gaussian multi-peaked probability distribution and a dynamical transition to an absorbing state. In the context of atherosclerosis, this dynamical transition to an absorbing state can be viewed as a minimal mechanism leading to the segregation of macrophages in lipid enriched regions and therefore to the formation of the atherosclerosis plaque.

Domaines: Equations aux dérivées partielles [math.AP]

Olivier Benichou, Nicolas Meunier, Sidney Redner, Raphael Voituriez. Non-Gaussianity and Dynamical Trapping in Locally Activated Random Walks. 2012. ⟨hal-00716339⟩