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Peer-reviewedCC BY-NC-NDInternational Mathematics Research Notices

Multiradial SLE with spiral: resampling property and boundary perturbation

  • Chongzhi Huang1
  • Eveliina Peltola2,3
  • Hao Wu1
  1. 1Yau Mathematical Sciences Center , Tsinghua University, Beijing 100084, China
  2. 2Department of Mathematics and Systems Analysis , School of Science, Aalto University, Espoo 02150, Finland
  3. 3Institute for Applied Mathematics , University of Bonn, Bonn 53115, Germany
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Abstract

We consider multiple radial Schramm–Loewner evolution (SLE) curves with various time parameterizations and possible spiraling behavior. We construct them by tilting independent radial SLEs with a suitable local martingale, generalizing the earlier construction by Healey and Lawler. We prove that the curves are almost surely transient (i.e., they emanate from boundary points and terminate at a common interior target point). We show that they enjoy the resampling property: conditional on all of the curves but one, the remaining curve is distributed as chordal SLE in the remaining domain. We also verify that the multiradial SLE measure satisfies a natural boundary perturbation property analogous to that of the known SLE variants, involving its partition function (which is finite). Interestingly, in the parlance of Coulomb gas formalism in conformal field theory, partition functions of multiradial SLE processes with spiral involve both electric and magnetic charges.

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Cite

BibTeXRIS
BibTeX
@article{huang2026multiradial,
  title = {{Multiradial SLE with spiral: resampling property and boundary perturbation}},
  author = {Chongzhi Huang and Eveliina Peltola and Hao Wu},
  journal = {International Mathematics Research Notices},
  year = {2026},
  month = jul,
  doi = {10.1093/imrn/rnag160},
  url = {https://doi.org/10.1093/imrn/rnag160},
  note = {CC BY-NC-ND},
}
RIS
TY  - JOUR
TI  - Multiradial SLE with spiral: resampling property and boundary perturbation
AU  - Chongzhi Huang
AU  - Eveliina Peltola
AU  - Hao Wu
PY  - 2026
DA  - 2026/07/02
JO  - International Mathematics Research Notices
DO  - 10.1093/imrn/rnag160
UR  - https://doi.org/10.1093/imrn/rnag160
AB  - We consider multiple radial Schramm–Loewner evolution (SLE) curves with various time parameterizations and possible spiraling behavior. We construct them by tilting independent radial SLEs with a suitable local martingale, generalizing the earlier construction by Healey and Lawler. We prove that the curves are almost surely transient (i.e., they emanate from boundary points and terminate at a common interior target point). We show that they enjoy the resampling property: conditional on all of the curves but one, the remaining curve is distributed as chordal SLE in the remaining domain. We also verify that the multiradial SLE measure satisfies a natural boundary perturbation property analogous to that of the known SLE variants, involving its partition function (which is finite). Interestingly, in the parlance of Coulomb gas formalism in conformal field theory, partition functions of multiradial SLE processes with spiral involve both electric and magnetic charges.
SN  - 1073-7928
SN  - 1687-0247
ER  -