4 papers
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…