Browsing by Author "Grange, P"

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    Run-and-tumble particles on a line with a fertile site
    (Journal of Physics A: Mathematical and Theoretical, 2021-08-13) Grange, P; Yao, X
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    Winding number of a Brownian particle on a ring under stochastic resetting
    (Journal of Physics A: Mathematical and Theoretical, 2022-04-19) Grange, P
    Abstract We consider a random walker on a ring, subjected to resetting at Poisson-distributed times to the initial position (the walker takes the shortest path along the ring to the initial position at resetting times). In the case of a Brownian random walker the mean first-completion time of a turn is expressed in closed form as a function of the resetting rate. The value is shorter than in the ordinary process if the resetting rate is low enough. Moreover, the mean first-completion time of a turn can be minimised in the resetting rate. At large time the distribution of winding numbers does not reach a steady state, which is in contrast with the non-compact case of a Brownian particle under resetting on the real line. The mean total number of turns and the variance of the net number of turns grow linearly with time, with a proportionality constant equal to the inverse of the mean first-completion time of a turn.