Generating constrained run-and-tumble trajectories – Archive ouverte HAL

Benjamin de Bruyne ¹ Satya N. Majumdar ¹ Grégory Schehr ² Satya Majumdar ¹

Benjamin de Bruyne, Satya N. Majumdar, Grégory Schehr, Satya Majumdar. Generating constrained run-and-tumble trajectories. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2021, 54 (38), pp.385004. ⟨10.1088/1751-8121/ac1d8e⟩. ⟨hal-03388311⟩

We propose a method to exactly generate bridge run-and-tumble trajectories that are constrained to start at the origin with a given velocity and to return to the origin after a fixed time with another given velocity. The method extends the concept of effective Langevin equations, valid for Markovian stochastic processes such as Brownian motion, to a non-Markovian stochastic process driven by a telegraphic noise, with exponentially decaying correlations. We obtain effective space-time dependent tumbling rates that implicitly accounts for the bridge constraint. We extend the method to other types of constrained run-and-tumble particles such as excursions and meanders. The method is implemented numerically and is shown to be very efficient.

• 1. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
• 2. LPTHE – Laboratoire de Physique Théorique et Hautes Energies