Optimal mean first-passage time of a Brownian searcher with resetting in one and two dimensions: experiments, theory and numerical tests

  title={Optimal mean first-passage time of a Brownian searcher with resetting in one and two dimensions: experiments, theory and numerical tests},
  author={F{\'e}lix Faisant and Benjamin Besga and A. N. Petrosyan and Sergio Ciliberto and Satya N. Majumdar},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
We experimentally, numerically and theoretically study the optimal mean time needed by a Brownian particle, freely diffusing either in one or two dimensions, to reach, within a tolerance radius R tol, a target at a distance L from an initial position in the presence of resetting. The reset position is Gaussian distributed with width σ. We derived and tested two resetting protocols, one with a periodic and one with random (Poissonian) resetting times. We computed and measured the full first… 

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  • Pascal Grange
  • Mathematics
    Journal of Physics A: Mathematical and Theoretical
  • 2022
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

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The optimal mean first-passage time as a function of the resetting period/rate for different values of the ratio b = L/$\sigma$ is studied and an interesting phase transtion at a critical value b = bc is found.

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Deterministic resetting typically leads to a lower search cost than in stochastic resetting, and several unexpected feature arise for searchers when the resetting is deterministic, including the search time being independent of $T$ for $1/T\to 0$ and the search cost being independentof $N$ over a suitable range of $N$.

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