A Gaussian free field approach to the natural parametrisation of SLE4

Vlad Margarint; Lukas Schoug

doi:10.1214/23-ECP563

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Home > Journals > Electron. Commun. Probab. > Volume 28 > Article

2023 A Gaussian free field approach to the natural parametrisation of

{SLE}_{4}

Vlad Margarint, Lukas Schoug

Author Affiliations +

Vlad Margarint,¹ Lukas Schoug²
¹University of North Carolina at Charlotte, United States of America
²University of Helsinki, Finland

Electron. Commun. Probab. 28: 1-13 (2023). DOI: 10.1214/23-ECP563

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Abstract

We construct the natural parametrisation of ${SLE}_{4}$ using the Gaussian free field, complementing the corresponding results for ${SLE}_{κ}$ for $κ \in (0, 4)$ by Benoist [2] and for $κ \in (4, 8)$ by Miller and Schoug [15].

Funding Statement

LS was supported by the Finnish Academy Centre of Excellence FiRST and the ERC starting grant 804166 (SPRS).

Acknowledgments

We thank Hao Wu for valuable input and an anonymous referee for helpful comments.

Citation

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Vlad Margarint. Lukas Schoug. "A Gaussian free field approach to the natural parametrisation of ${SLE}_{4}$ ." Electron. Commun. Probab. 28 1 - 13, 2023. https://doi.org/10.1214/23-ECP563