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On Conditioning Brownian Particles to Coalesce

Author

Listed:
  • Vitalii Konarovskyi

    (Universitätsstraße 25
    Universität Leipzig
    Institute of Mathematics of NAS of Ukraine)

  • Victor Marx

    (Universität Leipzig)

Abstract

We introduce the notion of a conditional distribution to a zero-probability event in a given direction of approximation and prove that the conditional distribution of a family of independent Brownian particles to the event that their paths coalesce after the meeting coincides with the law of a modified massive Arratia flow, defined in Konarovskyi (Ann Probab 45(5):3293–3335, 2017. https://doi.org/10.1214/16-AOP1137 ).

Suggested Citation

  • Vitalii Konarovskyi & Victor Marx, 2023. "On Conditioning Brownian Particles to Coalesce," Journal of Theoretical Probability, Springer, vol. 36(4), pages 2126-2164, December.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:4:d:10.1007_s10959-023-01267-4
    DOI: 10.1007/s10959-023-01267-4
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    References listed on IDEAS

    as
    1. Dorogovtsev, Andrey A. & Riabov, Georgii V. & Schmalfuß, Björn, 2020. "Stationary points in coalescing stochastic flows on R," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4910-4926.
    2. Kawasaki, Kyozi, 1994. "Stochastic model of slow dynamics in supercooled liquids and dense colloidal suspensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 208(1), pages 35-64.
    3. Blount, Douglas & Kouritzin, Michael A., 2010. "On convergence determining and separating classes of functions," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 1898-1907, September.
    Full references (including those not matched with items on IDEAS)

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