7 papers
Graph distance and percolation dimension of three-dimensional Brownian motion
Daisuke Shiraishi
We prove that the minimum Hausdorff dimension of a continuous curve joining to within the range of a three-dimensional Brownian motion is almost surely a det…
Collision properties of the four-dimensional random walk trace
David A. Croydon, Daisuke Shiraishi, Satomi Watanabe
We consider collisions of multiple random walks on the trace of a simple random walk on the four-dimensional integer lattice. For two independent walks (in continuous time), we app…
Tail exponents of the three-dimensional uniform spanning tree and Abelian sandpile
Xinyi Li, Runsheng Liu, Daisuke Shiraishi
We study the local geometry of the three-dimensional uniform spanning tree and its connection with the Abelian sandpile model. We obtain sharp tail exponents, up to subpolynomial e…
Largest-loop-first loop-erased random walk on
Daisuke Shiraishi, Satomi Watanabe
Let be a simple random walk on started at the origin. We study a loop-erasing procedure of that differs from Lawler's chronological loop-eras…
Convergence in natural parametrization of random walk frontier
Yifan Gao, Xinyi Li, Runsheng Liu +2
In this paper, we show that the frontier of planar random walk converges weakly under natural parametrization to that of planar Brownian motion. As an intermediate result, we also…
Sharp one-point estimates and Minkowski content for the scaling limit of three-dimensional loop-erased random walk
Sarai Hernandez-Torres, Xinyi Li, Daisuke Shiraishi
In this work, we consider the scaling limit of loop-erased random walk (LERW) in three dimensions and prove that the limiting occupation measure is equivalent to its -dimensiona…
Scaling limit of the occupation measure of random walk cut points
Yifan Gao, Xinyi Li, Petr Panov +1
We consider the occupation measure of the cut points of a simple random walk on a -dimensional cubic lattice for , and we show that the scaling limit of the occupation…