English

N-sided Radial Schramm-Loewner Evolution

Probability 2022-01-07 v2

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 nn-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 nn-tuples of paths has a limit. The limit measure can be described as nn 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.

Cite

@article{arxiv.2002.04128,
  title  = {N-sided Radial Schramm-Loewner Evolution},
  author = {Vivian Olsiewski Healey and Gregory F. Lawler},
  journal= {arXiv preprint arXiv:2002.04128},
  year   = {2022}
}
R2 v1 2026-06-23T13:37:38.451Z