Universal survival probability for a d-dimensional run-and-tumble particle

Statistical Physics and Complexity Group meeting

Universal survival probability for a d-dimensional run-and-tumble particle

  • Event time: 11:30am until 12:30pm
  • Event date: 27th January 2021
  • Speaker: (Université de Paris-Sud)
  • Location: Online - see email

Event details

We consider an active run-and-tumble particle (RTP) in d dimensions and compute exactly the probability S(t) that the x-component of the position of the RTP does not change sign up to time t. When the tumblings occur at a constant rate, we show that S(t) is independent of d for any finite time t (and not just for large t), as a consequence of the celebrated Sparre Andersen theorem for discrete-time random walks in one dimension. Moreover, we show that this universal result holds for a much wider class of RTP models in which the speed v of the particle after each tumbling is random, drawn from an arbitrary probability distribution. We further demonstrate, as a consequence, the universality of the record statistics in the RTP problem.