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

Abstract

We consider multiple chordal Schramm-Loewner evolution (SLE) with $\hat{I}º\in (0,4]$. 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].

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