Studying run-and-tumble particles by piecewise deterministic Markov processes

Run-and-tumble particles (RTP) are persistent random processes which follow ballistic trajectories whose directions are reoriented following a Poisson process. Their analytical study is attracting a growing interest, as they embody a good model of active particles, as bacteria or active engineered material. By the persistence of the displacements of such active particles, the phenomenology of observed behaviors is rich, from deviation from the Boltzmann distribution to motility-phase induced separation. Various theoretical methods have then be derived but there still is no systematic method for deriving directly from the microscopic details the exact form of the stationary distribution, whereas the most outstanding challenge for the whole field of active matter appears to be the question of the precise impact of such microscopic details.

In this talk, I will first present how RTP can be characterized by piecewise deterministic Markov processes. Then, building on some recent insights gained from the use of PDMP for Monte Carlo sampling of equilibrium systems, I will show how the PDMP characterization allows for a direct derivation of the different classes of stationary distribution of a two-RTP system.