A Gaussian free field approach to the natural parametrisation of SLE${}_4$

Abstract

We construct the natural parametrisation of SLE${}_4$ using the Gaussian free field, complementing the corresponding results for SLE${}_{\kappa }$ for $\kappa \in (0,4)$ by Benoist and for $\kappa \in (4,8)$ by Miller and Schoug.

arXiv comment13 pages. Final version, to appear in Electron. Comm. Probab