The Hölder continuity of the scaling limit of three-dimensional loop-erased random walk

Xinyi Li; Daisuke Shiraishi

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arXiv · 2111.04977

The Hölder continuity of the scaling limit of three-dimensional loop-erased random walk

Xinyi Li·Daisuke Shiraishi

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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 $h$-Hölder continuous almost surely for all $h < 1/β$, while not $1/β$-Hölder continuous almost surely.

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Xinyi Li, Daisuke Shiraishi. 2022-10-26. The Hölder continuity of the scaling limit of three-dimensional loop-erased random walk. https://arxiv.org/abs/2111.04977

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