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Limits of Radial Multiple SLE and a Burgers–Loewner Differential Equation

Author

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  • Ikkei Hotta

    (Yamaguchi University)

  • Sebastian Schleißinger

    (University of Wuerzburg)

Abstract

We consider multiple radial SLE as the number of curves tends to infinity. We give conditions that imply the tightness of the associated processes given by the Loewner equation. In the case of equal weights, the infinite-slit limit is described by a Loewner equation whose Herglotz vector field is given by a Burgers differential equation. Furthermore, we investigate a more general form of the Burgers equation. On the one hand, it appears in connection with semigroups of probability measures on $${\mathbb {T}}$$ T with respect to free convolution. On the other hand, the Burgers equation itself is also a Loewner differential equation for certain subordination chains.

Suggested Citation

  • Ikkei Hotta & Sebastian Schleißinger, 2021. "Limits of Radial Multiple SLE and a Burgers–Loewner Differential Equation," Journal of Theoretical Probability, Springer, vol. 34(2), pages 755-783, June.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:2:d:10.1007_s10959-020-00996-0
    DOI: 10.1007/s10959-020-00996-0
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    References listed on IDEAS

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    1. Andrea del Monaco & Sebastian Schleißinger, 2016. "Multiple SLE and the complex Burgers equation," Mathematische Nachrichten, Wiley Blackwell, vol. 289(16), pages 2007-2018, November.
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    Cited by:

    1. Chen, Jiaming & Margarint, Vlad, 2022. "Perturbations of multiple Schramm–Loewner evolution with two non-colliding Dyson Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 151(C), pages 553-570.

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    1. Chen, Jiaming & Margarint, Vlad, 2022. "Perturbations of multiple Schramm–Loewner evolution with two non-colliding Dyson Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 151(C), pages 553-570.

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