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

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2022-04-19

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<jats:title>Abstract</jats:title> <jats:p>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.</jats:p>

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10.1088/1751-8121/ac57cf

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Grange, P (2022). Winding number of a Brownian particle on a ring under stochastic resetting. Journal of Physics A: Mathematical and Theoretical, 55(15). pp. 155003–155003. 10.1088/1751-8121/ac57cf Retrieved from https://hdl.handle.net/10161/29033.

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Grange

Pascal Grange

Associate Professor of Mathematics at Duke Kunshan University

A theoretical physicist by training, Pascal Grange is interested in quantitative models of systems with many degrees of freedom. His current field of research is the statistical physics of out-of-equilibrium systems (this class of systems includes living systems). His teaching interests at Duke Kunshan University include probability, differential equations and geometry.


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