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