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

Abstract

Let $\beta$ 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 $h<1/\beta$, while not $1/\beta$-Hölder continuous almost surely.

arXiv comment37 pages, 7 figures