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N-sided radial Schramm–Loewner evolution

Abstract

We use the interpretation of the Schramm–Loewner evolution as a limit of path measures tilted by a loop term in order to motivate the definition of n-radial SLE going to a particular point. In order to justify the definition we prove that the measure obtained by an appropriately normalized loop term on n-tuples of paths has a limit. The limit measure can be described as n paths moving by the Loewner equation with a driving term of Dyson Brownian motion. While the limit process has been considered before, this paper shows why it naturally arises as a limit of configurational measures obtained from loop measures.

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Correspondence to Gregory F. Lawler.

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In memory of Harry Kesten whose deep insights paved the way for us today.

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Research supported in part by NSF DMS-1246999. Research supported by NSF DMS-1513036.

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Healey, V.O., Lawler, G.F. N-sided radial Schramm–Loewner evolution. Probab. Theory Relat. Fields 181, 451–488 (2021). https://doi.org/10.1007/s00440-021-01033-9

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  • DOI: https://doi.org/10.1007/s00440-021-01033-9

Mathematics Subject Classification

  • 60J67 Stochastic (Schramm-) Loewner Evolution