Archive ouverte HAL – Run and tumble particle under resetting: a renewal approach

Martin R. Evans 1 Satya N. Majumdar 2

Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2018, 51 (47), pp.475003. 〈10.1088/1751-8121/aae74e〉

We consider a particle undergoing run and tumble dynamics, in which its velocity stochastically reverses, in one dimension. We study the addition of a Poissonian resetting process occurring with rate $r$. At a reset event the particle's position is returned to the resetting site $X_r$ and the particle's velocity is reversed with probability $\eta$. The case $\eta = 1/2$ corresponds to position resetting and velocity randomization whereas $\eta =0$ corresponds to position-only resetting. We show that, beginning from symmetric initial conditions, the stationary state does not depend on $\eta$ i.e. it is independent of the velocity resetting protocol. However, in the presence of an absorbing boundary at the origin, the survival probability and mean time to absorption do depend on the velocity resetting protocol. Using a renewal equation approach, we show that the the mean time to absorption is always less for velocity randomization than for position-only resetting.

  • 1. SUPA, School of Physics, University of Edinburgh
  • 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques