arXiv subjects

Xiangyi Liu

Publications and source records attributed to Xiangyi Liu.

2 recordsLinked to original sources

arXiv2025

Convergence in natural parametrization of random walk frontier

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 show the convergence of the renormalized occupation measure.

math.PR↗

arXiv2024

A boundary Harnack principle and its application to analyticity of 3D Brownian intersection exponents

We show that a domain in $\mathbb{R}^3$ with the trace of a 3D Brownian motion removed almost surely satisfies the boundary Harnack principle (BHP). Then, we use it to prove that the intersection exponents for 3D Brownian motion are analytic.

math.PR↗