22 citations · 51 across the 23 of their papers we have counts for
5 papers · 1 filter
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…
Shape theorem and surface fluctuation for Poisson cylinders
Marcelo Hilario, Xinyi Li, Petr Panov
In this work, we prove a shape theorem for Poisson cylinders and give a power law bound on surface fluctuations. We prove that for any , conditioned on the origin b…
Natural parametrization of percolation interface and pivotal points
Nina Holden, Xinyi Li, Xin Sun
We prove that the interface of critical site percolation on the triangular lattice converges to SLE in its natural parametrization, where the discrete interface is parametrized…
Minkowski content of Brownian cut points
Nina Holden, Gregory F. Lawler, Xinyi Li +1
Let , , be a Brownian motion in , . We say that is a cut point for if for some such that and $W (t…