Multiple SLEs and Dyson Brownian motion: transition density and Green's function

Chongzhi Huang; Hao Wu; Lu Yang

Multiple SLEs and Dyson Brownian motion: transition density and Green's function

Probability 2025-09-03 v4

Authors: Chongzhi Huang , Hao Wu , Lu Yang

Abstract

We consider multiple chordal Schramm-Loewner evolution (SLE) with $\kappa\in (0,4]$ . Under common-time parameterization, we show that the transition density of the driving function of multiple chordal SLEs can be given by the transition density of Dyson Brownian motion and Green's function. This is a companion paper of [FWY24].

Keywords

brownian motion

Cite

@article{arxiv.2311.06789,
  title  = {Multiple SLEs and Dyson Brownian motion: transition density and Green's function},
  author = {Chongzhi Huang and Hao Wu and Lu Yang},
  journal= {arXiv preprint arXiv:2311.06789},
  year   = {2025}
}

Comments

22 pages. We found gaps in the previous version. Now we restrict our conclusion for $\kappa\le 4$ and reformulate Theorem~1.4

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