Extremal statistics of a one-dimensional run and tumble particle with an absorbing wall

Abstract We study the extreme value statistics of a run and tumble particle (RTP) in one dimension till its first passage to origin starting from position x 0 ( > stretchy="false">) . This model has recently drawn lot interest due biological application modelling motion certain species bacteria. Herein, we analytically exact time-dependent propagators for single RTP finite interval with absorbing conditions at two ends. By exploiting path decomposition technique, use these appropriately compute joint distribution $\mathcal{P}(M,t_m)$?> maximum displacement M first-passage time t m which this is achieved exactly. The corresponding marginal distributions $\mathbb{P}_M(M)$?> P M $P_M(t_m)$?> P t m are studied separately verified numerically. In particular, find that interesting asymptotic forms large small While , depends sensitively on initial velocity direction σ i completely different Brownian motion, decay same as although amplitude crucially x 0 verify all our analytical results high precision by numerical simulations.