TY - JOUR

T1 - Winding number of a Brownian particle on a ring under stochastic resetting

AU - Grange, Pascal

N1 - Publisher Copyright:
© 2022 IOP Publishing Ltd.

PY - 2022/4/19

Y1 - 2022/4/19

N2 - 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.

AB - 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.

KW - random walks

KW - stochastic resetting

KW - topological effects

UR - http://www.scopus.com/inward/record.url?scp=85126720814&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/ac57cf

DO - 10.1088/1751-8121/ac57cf

M3 - Article

AN - SCOPUS:85126720814

SN - 1751-8113

VL - 55

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 15

M1 - 155003

ER -