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math.PR2021
The Hölder continuity of the scaling limit of three-dimensional loop-erased random walk
Xinyi Li, Daisuke Shiraishi
Let be the growth exponent of the loop-erased random walk (LERW) in three dimensions. We prove that the scaling limit of 3D LERW is -Hölder continuous almost surely for all…
math.PR2021
Scaling limit for random walk on the range of random walk in four dimensions
David A. Croydon, Daisuke Shiraishi
We establish scaling limits for the random walk whose state space is the range of a simple random walk on the four-dimensional integer lattice. These concern the asymptotic behavio…