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

Grange, Pascal

doi:10.1088/1751-8121/ac57cf

Cited by 2 publications

(2 citation statements)

References 39 publications

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“…Stochastic resetting induces a renewal structure, which allows to work out (the Laplace transform of) the probability of the configurations in the system undergoing resetting, in terms of the probability of the configurations in the ordinary system. This reasoning has yielded exact results on a variety of stochastic processes and out-of-equlibrium physical systems (including population dynamics, reaction-diffusion systems and active particles) [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. For a review, see [21] and references therein.…”

Section: Introductionmentioning

confidence: 98%

Voter model under stochastic resetting

Grange¹

2022

Preprint

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The voter model is a toy model of consensus formation based on nearest-neighbour interactions. Each voter is endowed with a Boolean variable (a binary opinion) that flips randomly at a rate set according to the opinions of the nearest neighbours. In this paper we subject the system to local resetting by considering stubborn voters. In addition to the usual dynamics, voters revert independently to their initial opinion according to a Poisson process of fixed intensity. The resulting kinetic equations for the average magnetization and two-point function of the model are derived and solved in closed form. They are formally identical to the heat equation coupled to a thermostat, whose temperature profile is induced by the initial conditions. In the case of initial conditions consisting of a single decided voter at the origin in a environment full of undecided voters, the average magnetization evolves as the probability density of a random walker with stochastic resetting to the origin. However, the long-time behaviour of the two-point function contains terms terms that cannot be obtained from a renewal argument. As a result, the steady-state densiity of domain walls can be extremized as a function of the resetting rate.

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Section: Introductionmentioning

confidence: 98%

Voter model under stochastic resetting

Grange¹

2022

Preprint

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“…Many further aspects of the effect of resetting on stochastic processes have been explored in recent years (see e.g. [6][7][8][9][10][11][12][13][14][15][16][17][18]).…”

Section: Introductionmentioning

confidence: 99%

The cost of stochastic resetting

Sunil,

Blythe,

Evans

et al. 2023

J. Phys. A: Math. Theor.

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Resetting a stochastic process has been shown to expedite the completion time of some complex tasks, such as finding a target for the first time. Here we consider the cost of resetting by associating to each reset a cost, which is a function of the distance travelled during the reset event. We compute the Laplace transform of the joint probability of first passage time $t_f$, number of resets $N$ and total resetting cost $C$, and use this to study the statistics of the total cost and also the time to completion ${\mathcal T} = C + t_f$. We show that in the limit of zero resetting rate, the mean total cost is finite for a linear cost function, vanishes for a sub-linear cost function and diverges for a super-linear cost function. This result contrasts with the case of no resetting where the cost is always zero. We also find that the resetting rate which optimizes the mean time to completion may be increased or decreased with respect to the case of no resetting cost according to the choice of cost function. For the case of an exponentially increasing cost function, we show that the mean total cost diverges at a finite resetting rate. We explain this by showing that the distribution of the cost has a power-law tail with a continuously varying exponent that depends on the resetting rate.

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

Cited by 2 publications

References 39 publications

Voter model under stochastic resetting

Voter model under stochastic resetting

The cost of stochastic resetting

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