Abstract
Let β be the growth exponent of the loop-erased random walk (LERW) in three dimensions. We prove that the scaling limit of 3D LERW is almost surely h-Hölder continuous for all , but not -Hölder continuous.
Funding Statement
XL’s research is supported by the National Key R&D Program of China (No. 2020YFA0712900 and No. 2021YFA1002700) and NSFC (No. 12071012). DS would like to thank David Croydon for his kind explanation of results and techniques in [2]. The proof of the second claim of the main theorem is inspired by the discussion. DS is supported by a JSPS Grant-in-Aid for Early-Career Scientists, 18K13425 and JSPS KAKENHI Grant Number 17H02849 and 18H01123.
Acknowledgments
The authors thank two anonymous referees for their careful reading and numerous helpful comments on an earlier draft of this work.
Citation
Xinyi Li. Daisuke Shiraishi. "The Hölder continuity of the scaling limit of three-dimensional loop-erased random walk." Electron. J. Probab. 27 1 - 37, 2022. https://doi.org/10.1214/22-EJP869
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