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Asymptotic Formulas for Extreme Statistics of Escape Times in 1, 2 and 3-Dimensions

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A Correction to this article was published on 09 June 2020

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Abstract

The first of N identical independently distributed (i.i.d.) Brownian trajectories that arrives to a small target sets the time scale of activation, which in general is much faster than the arrival to the target of a single trajectory only. Analytical asymptotic expressions for the minimal time is notoriously difficult to compute in general geometries. We derive here asymptotic laws for the probability density function of the first and second arrival times of a large number N of i.i.d. Brownian trajectories to a small target in 1, 2 and 3-dimensions and study their range of validity by stochastic simulations. The results are applied to activation of biochemical pathways in cellular biology.

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  • 09 June 2020

    In section 5.1 entitled ���The shortest NEP from a bounded domain in prviously.

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Acknowledgements

We thank C. Guerrier for her help in designing the two-dimensional simulations. This research was supported by the Foundation pour la Recherche Médicale—Équipes FRM 2016 grant DEQ20160334882.

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Authors and Affiliations

  1. Applied Mathematics and Computational Biology, Ecole Normale Supérieure, 46 rue d’Ulm, 75005, Paris, France

    K. Basnayake & D. Holcman

  2. Department of Applied Mathematics, Tel-Aviv University, 69978, Tel Aviv, Israel

    Z. Schuss

Authors
  1. K. Basnayake
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  2. Z. Schuss
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  3. D. Holcman
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Correspondence to D. Holcman.

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Communicated by Paul Newton.

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Basnayake, K., Schuss, Z. & Holcman, D. Asymptotic Formulas for Extreme Statistics of Escape Times in 1, 2 and 3-Dimensions. J Nonlinear Sci 29, 461–499 (2019). https://doi.org/10.1007/s00332-018-9493-7

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  • DOI: https://doi.org/10.1007/s00332-018-9493-7

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