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

Ikkei Hotta () and Sebastian Schleißinger ()
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Ikkei Hotta: Yamaguchi University
Sebastian Schleißinger: University of Wuerzburg

Journal of Theoretical Probability, 2021, vol. 34, issue 2, 755-783

Abstract: 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.

Keywords: Schramm–Loewner evolution; multiple SLE; complex Burgers equation; free probability; infinitely divisible distributions; 37L05; 46L54; 60J67 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-020-00996-0

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