12 citations · 18 across the 10 of their papers we have counts for
13 papers
Graph distance and effective resistance of the random walk trace in four and five dimensions
Arka Adhikari, Izumi Okada, Daisuke Shiraishi
In this paper, we prove that the fluctuations of the graph distance and the effective resistance on the trace of a random walk in four and five dimensions converge in distribution…
On the size of earthworm's trail
Krzysztof Burdzy, Shi Feng, Daisuke Shiraishi
We investigate the number of holes created by an ``earthworm'' moving on the two-dimensional integer lattice. The earthworm is modeled by a simple random walk. At the initial time,…
Volume and heat kernel fluctuations for the three-dimensional uniform spanning tree
Daisuke Shiraishi, Satomi Watanabe
Let be the uniform spanning tree on . We show the occurrence of log-logarithmic fluctuations around the leading order for the volume of intrinsic ball…
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…
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…
The number of spanning clusters of the uniform spanning tree in three dimensions
Omer Angel, David A. Croydon, Sarai Hernandez-Torres +1
Let be the uniform spanning tree on . A spanning cluster of is a connected component of the restriction of to th…
Scaling limits of the three-dimensional uniform spanning tree and associated random walk
Omer Angel, David A. Croydon, Sarai Hernandez-Torres +1
We show that the law of the three-dimensional uniform spanning tree (UST) is tight under rescaling in a space whose elements are measured, rooted real trees, continuously embedded…
Convergence of three-dimensional loop-erased random walk in the natural parametrization
Xinyi Li, Daisuke Shiraishi
In this work we consider loop-erased random walk (LERW) and its scaling limit in three dimensions, and prove that 3D LERW parametrized by renormalized length converges to its scali…
One-point function estimates for loop-erased random walk in three dimensions
Xinyi Li, Daisuke Shiraishi
In this work, we consider loop-erased random walk (LERW) in three dimensions and give an asymptotic estimate on the one-point function for LERW and the non-intersection probability…
Hausdorff dimension of the scaling limit of loop-erased random walk in three dimensions
Daisuke Shiraishi
Let be the length (number of steps) of the loop-erasure of a simple random walk up to the first exit from a ball of radius centered at its starting point. It is shown i…
On Brownian motion, simple paths, and loops
Artem Sapozhnikov, Daisuke Shiraishi
We provide a decomposition of the trace of the Brownian motion into a simple path and an independent Brownian soup of loops that intersect the simple path. More precisely, we prove…
Growth exponent for loop-erased random walk in three dimensions
Daisuke Shiraishi
We show the existence of the growth exponent for loop-erased random walk in three dimensions.
Two-sided random walks conditioned to have no intersections
Daisuke Shiraishi
Let be independent simple random walks in () started at the origin. We construct two-sided random walk paths conditioned that $S^{1}[0,\infty)…